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Class 12-commerce NCERT Solutions Maths Chapter 7: Integrals

Integrals Exercise Ex. 7.1

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Solution 22

Integrals Exercise Ex. 7.2

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begin mathsize 12px style sin open parentheses ax plus straight b close parentheses cos open parentheses ax plus straight b close parentheses equals fraction numerator 2 sin open parentheses ax plus straight b close parentheses cos open parentheses ax plus straight b close parentheses over denominator 2 end fraction equals fraction numerator sin 2 open parentheses ax plus straight b close parentheses over denominator 2 end fraction Let space 2 open parentheses ax plus straight b close parentheses equals straight t 2 adx equals dt rightwards double arrow integral fraction numerator sin 2 open parentheses ax plus straight b close parentheses over denominator 2 end fraction dx equals 1 half integral fraction numerator sint space dt over denominator 2 straight a end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator 4 straight a end fraction open square brackets negative cost close square brackets plus straight C space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator negative 4 straight a end fraction cos 2 open parentheses ax plus straight b close parentheses plus straight C end style

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Solution 32

Let sin x + cos x = t then (cos x - sin x) dx = dt

 

 

Solution 33

Put cos x - sin x = t then (- sin x - cos x)dx = dt

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Integrals Exercise Ex. 7.3

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Solution 24

Integrals Exercise Ex. 7.4

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Solution 23

 

begin mathsize 12px style straight I subscript 2 equals integral fraction numerator 1 over denominator open parentheses straight x plus 2 close parentheses squared plus open parentheses square root of 6 close parentheses squared end fraction dx space space space space space equals log open vertical bar straight x plus 2 plus square root of straight x squared plus 4 straight x plus 10 end root close vertical bar space space... left parenthesis 3 right parenthesis end style
 
 
 

Solution 24

Solution 25

begin mathsize 12px style straight I equals integral fraction numerator 1 over denominator square root of negative 4 open parentheses straight x squared minus begin display style fraction numerator 9 straight x over denominator 4 end fraction end style plus begin display style 81 over 64 end style minus begin display style 81 over 64 end style close parentheses end root end fraction dx end style

 

Integrals Exercise Ex. 7.5

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Solution 23

Integrals Exercise Ex. 7.6

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Solution 24

Integrals Exercise Ex. 7.7

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Integrals Exercise Ex. 7.8

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Solution 17

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Solution 22

Integrals Exercise Ex. 7.9

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Solution 10

Integrals Exercise Ex. 7.10

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Integrals Exercise Misc. Ex.

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Solution 40

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