UP Board Solutions for Class 12 Maths Chapter 7 Integrals

UP Board Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन) are part of UP Board Solutions for Class 12 Maths. Here we have given UP Board Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन)

Board UP Board
Textbook NCERT
Class Class 12
Subject Maths
Chapter Chapter 7
Chapter Name Integrals
Exercise Ex 7.1, Ex 7.2, Ex 7.3, Ex 7.4, Ex 7.5, Ex 7.6, Ex 7.7, Ex 7.8, Ex 7.9, Ex 7.10, Ex 7.11
Number of Questions Solved 228
Category UP Board Solutions

UP Board Solutions for Class 12 Maths Chapter 6 Application of Derivatives

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, [latex ]\frac { d }{ dx }[/latex] cos2x = -2 sin 2x
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 1

प्रश्न 2.
cos 3x
हल-
∫cos 3x dx
हम जानते हैं कि,
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 2

UP Board Solutions

प्रश्न 3.
e2x
हल-
∫e2x dx
हम जानते हैं कि,
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 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 image 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 image 5

निम्नलिखित समाकलनों को ज्ञात कीजिए।

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

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

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 image 9

प्रश्न 9.
∫(2x² + ex) dx
हल-
∫(2x² + ex) dx = 2∫x² dx + ∫ex dx
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 10

प्रश्न 10.
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प्रश्न 11.
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प्रश्न 12.
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प्रश्न 13.
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हल-
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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 image 19

प्रश्न 15.
∫√x(3x² + 2x + 3)dx
हल-
∫√x(3x² + 2x + 3)dx
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 20

प्रश्न 16.
∫(2x – 3cosx + ex)dx
हल-
∫(2x – 3cosx + ex)dx
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 21

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 image 22
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 23

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.
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प्रश्न 20.
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प्रश्न 21 एवं 22 में सही उत्तर का चयन कीजिए

प्रश्न 21
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प्रश्न 22
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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 image 33
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प्रश्न 2.
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प्रश्न 3.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 37
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 38

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 image 39

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 40
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प्रश्न 7.
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प्रश्न 8.
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प्रश्न 9.
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प्रश्न 10.
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प्रश्न 11.
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हल-
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प्रश्न 12.
(x3 – 1)1/3 x5
हल-
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प्रश्न 13.
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प्रश्न 14
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प्रश्न 15
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प्रश्न 16.
e2x+3
हल-
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प्रश्न 17.
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प्रश्न 18.
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प्रश्न 19.
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प्रश्न 20.
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हल-
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प्रश्न 21.
tan²(2x – 3)
हल-
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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 image 71

प्रश्न 23.
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प्रश्न 24.
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प्रश्न 25.
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प्रश्न 26.
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प्रश्न 27.
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प्रश्न 28.
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हल-
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प्रश्न 29.
cot x log sin x
हल-
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प्रश्न 30.
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प्रश्न 31.
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प्रश्न 32.
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प्रश्न 33.
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प्रश्न 34.
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प्रश्न 35.
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प्रश्न 36.
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प्रश्न 37.
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प्रश्न 38.
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प्रश्न 39.
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हल-
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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 image 107

प्रश्न 2.
sin 3x cos 4x dx
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 108

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 image 109

प्रश्न 4.
sin3 (2x + 1)
हल-
माना I = ∫sin3 (2x + 1) dx
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 110

प्रश्न 5.
sin3x cos3x
हल-
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प्रश्न 6.
sinx sin2x sin3x
हल-
माना I = ∫sinx sin2x sin3x
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 112

प्रश्न 7.
sin 4x sin 8x
हल-
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प्रश्न 8.
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प्रश्न 9.
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हल-
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प्रश्न 10.
sin xdx
हल-
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प्रश्न 11.
cos4 2x
हल-
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प्रश्न 12.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 120
हल-
माना
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 121
= ∫(1-cosx)dx = ∫1 dx – ∫ cosx dx
= x – sinx +C

UP Board Solutions

प्रश्न 13.
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प्रश्न 14.
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हल-
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प्रश्न 15.
tan3 2x sec 2x
हल-
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प्रश्न 16.
tan4 x
हल-
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प्रश्न 17.
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हल-
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प्रश्न 18.
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प्रश्न 19.
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प्रश्न 20.
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UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 137

प्रश्न 21.
sin-1 (cosx)
हल-
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प्रश्न 22.
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प्रश्न 23.
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प्रश्न 24.
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प्रश्नावली 7.4

प्रश्न 1 से 23 तक के फलनों का समाकलन कीजिए।

प्रश्न 1.
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प्रश्न 2.
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प्रश्न 3.
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प्रश्न 4.
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प्रश्न 5.
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प्रश्न 6.
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प्रश्न 7.
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प्रश्न 8.
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प्रश्न 9.
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प्रश्न 10.
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प्रश्न 11.
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प्रश्न 12.
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प्रश्न 13.
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प्रश्न 14.
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प्रश्न 15.
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प्रश्न 16.
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प्रश्न 17.
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प्रश्न 18.
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प्रश्न 19.
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प्रश्न 20.
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प्रश्न 21.
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प्रश्न 22.
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प्रश्न 23.
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प्रश्न 24.
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प्रश्न 25.
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हल-
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प्रश्नावली 7.5

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

प्रश्न 1.
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प्रश्न 2.
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प्रश्न 3.
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प्रश्न 4.
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प्रश्न 5.
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प्रश्न 6.
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प्रश्न 7.
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प्रश्न 8.
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प्रश्न 9.
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प्रश्न 10.
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प्रश्न 11.
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प्रश्न 12.
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प्रश्न 13.
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प्रश्न 14.
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प्रश्न 15.
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प्रश्न 16.
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प्रश्न 17.
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प्रश्न 18.
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प्रश्न 19.
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प्रश्न 20.
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प्रश्न 21.
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प्रश्न 22.
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प्रश्न 23.
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प्रश्नावली 7.6

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

UP Board Solutions

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 image 257
= – 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 image 258

प्रश्न 3.
x2 ex
हल-
माना I = ∫x2 ex dx
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 259

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 image 260

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 image 261

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 image 262

प्रश्न 7.
x sin-1 x
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 263

प्रश्न 8.
x tan-1x
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 264

UP Board Solutions

प्रश्न 9.
x cos-1 x
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 265

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 image 266

प्रश्न 11.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 267
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 268

प्रश्न 12.
x sec² x
हल-
माना I = ∫x sec² x dx
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 269
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 image 270

UP Board Solutions

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 image 271
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 272

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 image 273

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 image 274
हैल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 275
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 276

प्रश्न 18.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 277
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 278

प्रश्न 19.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 279
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 280

UP Board Solutions

प्रश्न 20.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 281
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 282

प्रश्न 21.
e2x sinx
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 283

प्रश्न 22.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 284
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 285

प्रश्न 23
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 286
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 287

UP Board Solutions

प्रश्न 24.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 288
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 289

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 image 290
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 291

प्रश्न 2.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 292
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 293

प्रश्न 3.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 294
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 295

प्रश्न 4.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 296
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 297

प्रश्न 5.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 298
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 299
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 300

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 301
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 302

UP Board Solutions

प्रश्न 7.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 303
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 304
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 305

प्रश्न 8.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 306
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 307

प्रश्न 9.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 308
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 309

UP Board Solutions

प्रश्न 10.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 310
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 311
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 312

प्रश्न 11.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 313
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 314

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 image 315
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 315

प्रश्न 2.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 316
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 317

प्रश्न 3.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 318
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 219

प्रश्न 4.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 320
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 321
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 322

UP Board Solutions

प्रश्न 5.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 323
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 324

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 325
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 326

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 image 327
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 328

प्रश्न 2.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 329
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 330

प्रश्न 3.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 331
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 4.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 333
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 334

प्रश्न 5.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 335
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 336

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 337
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 338

प्रश्न 7.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 339
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 340

प्रश्न 8.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 341
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 342
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 9.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 344
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 345

प्रश्न 10.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 346
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 347

प्रश्न 11.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 348
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 12.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 350
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 351

UP Board Solutions

प्रश्न 13.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 352
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 353
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 354

प्रश्न 14.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 355
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 15.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 357
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 358

प्रश्न 16.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 359
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 361
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 362

प्रश्न 17.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 363
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 18.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 365
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 366

प्रश्न 19.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 367
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 20.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 369
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 370

UP Board Solutions

प्रश्न 21.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 371
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 372

प्रश्न 22.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 373
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 374

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 image 375
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 376

प्रश्न 2.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 377
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 378
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 3.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 380
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 381

प्रश्न 4.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 382
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 383

UP Board Solutions

प्रश्न 5.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 384
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 385

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 386
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 387
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 7.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 389
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 390

प्रश्न 8.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 391
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 9.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 393
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 394
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 395
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 396

प्रश्न 10.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 397
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 398

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 image 399
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 2.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 401
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 402

UP Board Solutions

प्रश्न 3.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 403
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 4.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 405
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 406

प्रश्न 5.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 407
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 409
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 410

प्रश्न 7.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 411
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 412

UP Board Solutions

प्रश्न 8.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 413
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 414

प्रश्न 9.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 415
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 10.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 417
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 418
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 419

प्रश्न 11.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 420
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 12.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 422
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 423

प्रश्न 13.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 424
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 425

प्रश्न 14.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 426
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 427

UP Board Solutions

प्रश्न 15.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 428
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 429

प्रश्न 16.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 430
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 432
UP Board Solutions for Class 12 Maths Chapter 7 Integrals

प्रश्न 17.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 434
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 435

UP Board Solutions

प्रश्न 18.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 436
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 437

प्रश्न 19.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 438
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 439

प्रश्न 20.
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हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 441

प्रश्न 21.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 442
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals image 443

We hope the UP Board Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन) help you. If you have any query regarding UP Board Solutions for Class 12 Maths Chapter 7 Integrals (समाकलन), drop a comment below and we will get back to you at the earliest.

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