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int(0)^(pi//2) (cos theta)/(sqrt(4-sin^(...

`int_(0)^(pi//2) (cos theta)/(sqrt(4-sin^(2)theta))d theta` is equal to

A

`(pi)/(2)`

B

`(pi)/(6)`

C

`(pi)/(3)`

D

`(pi)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
B
` int_(0)^((pi)/(2)) (cos theta)/(sqrt(4-sin^(2) theta)) d theta`
`=[sin^(-1)((sin theta)/(2))]_(0)^(pi//2) = sin^(1-) ((1)/(2)) = (pi)/(6)`
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