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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
Let ` l = int_(0)^(pi//2) (cos theta)/(sqrt(4-sin^(2)theta)) d theta`
Put ` sin theta = t`
` rArr cos theta d theta = dt`
` :. l = int_(0)^(1) (dt)/(sqrt(4-t^(2)) )= [ sin ^(-1) t/2]_(0)^(1) = sin^(-1). 1/2 = pi/6`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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