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NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

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Last Updated on December 1, 2022 by Rohitash Kumawat

NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

समाकलन

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.1

    निम्नलिखित फलनों के प्रतिअवकलज ( समाकलन) निरीक्षण विधि द्वारा ज्ञात कीजिए।

    प्रश्न 1.
    sin 2x
    हल
    ∫sin 2x dx
    हम जानते हैं कि,  \frac { d }{ dx } cos2x = -2 sin 2x
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1

    प्रश्न 2.
    cos 3x
    हल
    ∫cos 3x dx
    हम जानते हैं कि,  \frac { d }{ dx } sin 3x = 3 cos 3x
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    e2x
    हल
    ∫e2x dx
    हम जानते हैं कि,
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3

    प्रश्न 4.
    (ax + b)²
    हल
    ∫(ax + b)² dx
    हम जानते हैं कि,
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4

    प्रश्न 5.
    sin 2x – 4e3x
    हल
    ∫(sin 2x -4e3x) dx = ∫sin 2x dx – 4∫e3x …(1)
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5

    निम्नलिखित समाकलनों को ज्ञात कीजिए।

    प्रश्न 6.
    ∫(4e3x + 1) dx
    हल
    ∫(4e3x + 1) dx = 4∫e3xdx + ∫1 dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1

    प्रश्न 8.
    ∫(ax² + bx + c) dx
    हल
    ∫(ax² + bx + c) dx = a∫x²dx + b∫xdx + c∫1 dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8

    प्रश्न 9.
    ∫(2x² + ex) dx
    हल
    ∫(2x² + ex) dx = 2∫x² dx + ∫ex dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    प्रश्न 12.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.1

    प्रश्न 13.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.1

    प्रश्न 14.
    ∫(1-x)√x dx
    हल
    ∫(1-x)√x dx
    =∫(√x-x√x)dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14

    प्रश्न 15.
    ∫√x(3x² + 2x + 3)dx
    हल
    ∫√x(3x² + 2x + 3)dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15

    प्रश्न 16.
    ∫(2x – 3cosx + ex)dx
    हल
    ∫(2x – 3cosx + ex)dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16

    प्रश्न 17.
    ∫(2x² – 3sinx + 5√x)dx
    हल
    ∫(2x² – 3sinx + 5√x)dx
    = 2∫x² dx – 3 ∫ sinx dx + 5∫√x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1

    प्रश्न 18.
    ∫secx (sec x + tan x) dx
    हल
    ∫sec x (sec x + tan x) dx
    = ∫(sec² x + sec x tan x) dx
    = ∫(sec² x dx
    = ∫sec x tan x dx
    tan x + sec x + C

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1

    प्रश्न 21 एवं 22 में सही उत्तर का चयन कीजिए

    प्रश्न 21
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21.1

    प्रश्न 22
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.2

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.2

    प्रश्न 1 से 37 तक के प्रश्नों में प्रत्येक फलने का समाकलन ज्ञात कीजिए

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1

    प्रश्न 4.
    sin x sin (cos x)
    हल
    मानी I = ∫ sin x sin (cos x) dx …(1)
    माना cos x = t, दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
    – sin x dx = dt ⇒ sin x dx = – dt
    ∴(1) से, I = ∫sin (cos x) (sin x) dx = -∫sint dt
    = cos t + C = cos (cos x) + C

    प्रश्न 5.
    sin (ax + b) cos (ax + b)
    हल
    माना I = ∫sin (ax + b) cos (ax + b) dx
    माना sin (ax + b) = t, दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
    a cos (ax + b) dx = dt
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8

    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.2

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    प्रश्न 12.
    (x3 – 1)1/3 x5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.1

    प्रश्न 13.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.1

    प्रश्न 14
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14.1

    प्रश्न 15
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15.1

    प्रश्न 16.
    e2x+3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16

    प्रश्न 17.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1

    प्रश्न 18.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.1

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1

    प्रश्न 21.
    tan²(2x – 3)
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21

    प्रश्न 22.
    sec²(7 – 4x)
    हल
    माना
    I = ∫sec²(7 – 4x) …(1)
    माना 7 – 4x = t, दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22

    प्रश्न 23.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23.1

    प्रश्न 24.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24.1

    प्रश्न 25.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 25
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 25.1

    प्रश्न 26.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 26
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 26.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 26.2

    प्रश्न 27.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 27
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 27.1

    प्रश्न 28.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 28
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 28.1

    प्रश्न 29.
    cot x log sin x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 29

    प्रश्न 30.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 30
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 30.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 30.2

    प्रश्न 31.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 31
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 31.1

    प्रश्न 32.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 32
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 32.1

    प्रश्न 33.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 33
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 33.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 33.2

    प्रश्न 34.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 34
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 34.1

    प्रश्न 35.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 35
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 35.1

    प्रश्न 36.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 36
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 36.1

    प्रश्न 37.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 37
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 37.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 37.2

    प्रश्न 38.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 38
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 38.1

    प्रश्न 39.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 39
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 39.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.3

    निर्देश- 1 से 22 तक के प्रश्नों में प्रत्येक का समाकलन ज्ञात कीजिए।

    प्रश्न 1.
    sin² (2x + 5)
    हल
    माना I = ∫sin ² (2x + 5) dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1

    प्रश्न 2.
    sin 3x cos 4x dx
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2

    प्रश्न 3.
    cos 2x cos 4x cos 6x dx
    हल
    cos 2x cos 4x cos 6x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3

    प्रश्न 4.
    sin3 (2x + 1)
    हल
    माना I = ∫sin3 (2x + 1) dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    sin3x cos3x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5

    प्रश्न 6.
    sinx sin2x sin3x
    हल
    माना I = ∫sinx sin2x sin3x

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6

    प्रश्न 7.
    sin 4x sin 8x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    प्रश्न 10.
    sin xdx
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10

    प्रश्न 11.
    cos4 2x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11

    प्रश्न 12.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.1
    हल
    माना
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    = ∫(1-cosx)dx = ∫1 dx – ∫ cosx dx
    = x – sinx +C

    प्रश्न 13.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.1

    प्रश्न 14.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14.1

    प्रश्न 15.
    tan3 2x sec 2x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15

    प्रश्न 16.
    tan4 x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16

    प्रश्न 17.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1

    प्रश्न 18.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.1

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.2

    प्रश्न 21.
    sin-1 (cosx)
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21

    प्रश्न 22.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.1

    प्रश्न 23.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23.1

    प्रश्न 24.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.4


    प्रश्न 1 से 23 तक के फलनों का समाकलन कीजिए।

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1

    प्रश्न 4.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.1

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.2

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    प्रश्न 12.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.1

    प्रश्न 13.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.2

    प्रश्न 14.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14.1

    प्रश्न 15.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15.1

    प्रश्न 16.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.1

    प्रश्न 17.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1

    प्रश्न 18.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.2

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.3

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.3

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1

    प्रश्न 21.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21.1

    प्रश्न 22.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.2

    प्रश्न 23.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23.1

    प्रश्न 24.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24.1

    प्रश्न 25.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 25
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 25.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.5

    प्रश्न 1 से 21 तक के प्रश्नों में परिमेय फलनों का समाकलन कीजिए

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.2

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2

    हल

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.2

    प्रश्न 4.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.1

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.2
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.2

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.2
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.2

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.2

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.2

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    प्रश्न 12.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.2

    प्रश्न 13.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.1

    प्रश्न 14.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14.1

    प्रश्न 15.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15.1

    प्रश्न 16.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.1

    प्रश्न 17.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1

    प्रश्न 18.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.2

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.2

    प्रश्न 21.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21.1

    प्रश्न 22.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.1

    प्रश्न 23.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.6


    प्रश्न 1 से 22 तक के प्रश्नों के फलनों का समाकलन कीजिए

    प्रश्न 1.
    फलन x sin x का x के सापेक्ष समाकल ज्ञात कीजिए।
    हल
    ∫x sin x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    = – x cos x + ∫cos x dx
    = – x cos x + sin x + C

    प्रश्न 2.
    x sin 3x
    हल
    माना I = ∫x.sin 3x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2

    प्रश्न 3.
    x2 ex
    हल
    माना I = ∫x2 ex dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3

    प्रश्न 4.
    फलन x log x का x के सापेक्ष समाकल ज्ञात कीजिए।
    हल
    ∫ x log x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4

    प्रश्न 5.
    x log 2x
    हल
    माना I = ∫x log 2x dx
    = ∫(log 2x).x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5

    प्रश्न 6.
    फलन x² log x का x के सापेक्ष समाकल ज्ञात कीजिए।
    हल
    माना I = ∫x² log x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6

    प्रश्न 7.
    x sin-1 x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7

    प्रश्न 8.
    x tan-1x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8

    प्रश्न 9.
    x cos-1 x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9

    प्रश्न 10.
    (sin-1x)2
    हल
    माना I = [(sin-1 x)2 dx ….(1)
    sin-1 x = θ ⇒ x = sinθ ⇒ dx = cos θ dθ
    ∴(1) से,
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    प्रश्न 12.
    x sec² x
    हल
    माना I = ∫x sec² x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    x को पहला फलन तथा sec²x को दूसरा फलन लेकन खण्डश: समाकलन करने पर,
    = x tan x – ∫1. tan x dx
    = x tan x + log|cos x| + C

    प्रश्न 13.
    tan-1 x
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13

    प्रश्न 14.
    x(log x)²
    हल
    माना I = ∫x (log x)² dx
    = ∫(log x)².x dx
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14.1

    प्रश्न 15.
    (x² + 1) log x
    हल
    माना I = ∫(x² + 1) log x dx
    = ∫log x. (x² + 1) dx
    (log x) को पहला फलन तथा (x² + 1) को दूसरा फलन लेकर खण्डश: समाकलन करने पर,
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15

    प्रश्न 16.
    e(sinx + cosx)
    हल
    ex sinx = t
    ⇒ e(sinx + cosx)dx = dt
    = ∫ex(sinx + cosx)dx = ∫dt = t + c
    = ex sinx + c

    प्रश्न 17
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    हैल-
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.2

    प्रश्न 18.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.1

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1

    प्रश्न 21.
    e2x sinx
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21

    प्रश्न 22.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.1

    प्रश्न 23
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 23.1

    प्रश्न 24.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 24.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.7

    प्रश्न 1 से 9 तक के फलनों का समाकलन कीजिए

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1

    प्रश्न 4.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.1

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.2

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10

    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.8

    योगों की सीमा के रूप में निम्नलिखित निश्चित समाकलनों का मान ज्ञात कीजिए।

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1

    प्रश्न 4.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.1

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.9

    1 से 20 तक के प्रश्नों में निश्चित समाकलनों का मान ज्ञात कीजिए

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1

    प्रश्न 4.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.1

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.2

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    प्रश्न 12.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.1

    प्रश्न 13.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.2

    प्रश्न 14.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14.1

    प्रश्न 15.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15.2

    प्रश्न 16.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.2
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.3

    प्रश्न 17.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1

    प्रश्न 18.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.1

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1

    प्रश्न 21.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21.1

    प्रश्न 22.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.10

    प्रश्न 1 से 8 तक के प्रश्नों में समाकलनों का मान प्रतिस्थापन का उपयोग करते हुए ज्ञात कीजिए।

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.2

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1

    प्रश्न 4.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.2

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.2

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    NCERT Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

    प्रश्नावली 7.11

    निश्चित समाकलनों में गुणधर्मों का उपयोग करते हुए 1 से 19 तक के प्रश्नों में समाकलनों का मान ज्ञात कीपिए—

    प्रश्न 1.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 1.1

    प्रश्न 2.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 2.1

    प्रश्न 3.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 3.1

    प्रश्न 4.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 4.1

    प्रश्न 5.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 5.1

    प्रश्न 6.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 6.1

    प्रश्न 7.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 7.1

    प्रश्न 8.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 8.1

    प्रश्न 9.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 9.1

    प्रश्न 10.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.1

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 10.2

    प्रश्न 11.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 11.1

    प्रश्न 12.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 12.1

    प्रश्न 13.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 13.1

    प्रश्न 14.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 14.1

    प्रश्न 15.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 15.1

    प्रश्न 16.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16

    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.2

    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 16.3

    प्रश्न 17.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 17.1

    प्रश्न 18.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18

    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.1
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 18.2

    प्रश्न 19.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 19.1

    प्रश्न 20.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20.1

    प्रश्न 21.
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21
    हल
    UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21.1

    सभी प्रश्नावली कक्षा १२वीं गणित की

    प्रश्नावली संख्याप्रश्नावली नाम
    प्रश्नावली 1सम्बन्ध एवं फलन
    प्रश्नावली 2प्रतिलोम त्रिकोणमितीय फलन
    प्रश्नावली 3आव्यूह
    प्रश्नावली 4सारणिक
    प्रश्नावली 5सांतत्य तथा अवकलनीयता
    प्रश्नावली 6अवकलज के अनुप्रयोग
    प्रश्नावली 7समाकलन
    प्रश्नावली 8समाकलनों के अनुप्रयोग
    प्रश्नावली 9अवकल समीकरण
    प्रश्नावली 10सदिश बीजगणित
    प्रश्नावली 11त्रिविमीय ज्यामिति
    प्रश्नावली 12रैखिक प्रोग्रामन
    प्रश्नावली 13प्रायिकता
    NCERT Solutions for Class 12 Maths गणित

    सभी प्रश्नावली कक्षा १२वीं गणित की

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