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int(0)^(pi//2)sqrt(1+cos2x)dx=?...

`int_(0)^(pi//2)sqrt(1+cos2x)dx=?`

A

`sqrt(2)`

B

`(3)/(2)`

C

`sqrt(3)`

D

`2`

Text Solution

Verified by Experts

`I=int_(0)^(pi//2)sqrt(2cos^(2)x)dx=sqrt(2)int_(0)^(pi//2)cosxdx=sqrt(2)[sinx]_(0)^(pi//2)=sqrt(2)`.
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