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The value of int (0)^(pi//2) ((sin x + ...

The value of ` int _(0)^(pi//2) ((sin x + cos x)^(2))/(sqrt(1+sin 2x) dx` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int_(0)^(pi//2)((sinx+cosx)^(2))/(sqrt(sin^(2)x+cos^(2)x+2sinxcosx))dx`
`=int_(0)^(pi//2)((sinx+cosx)^(2))/(sqrt((sinx+cosx)^(2)))dx`
`=int_(0)^(pi//2)(sinx+cosx)dx`
`=[-cosx+sinx]_(0)^(pi//2)=-0+1+1-0=2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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