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The value of I=int(-1)^(1)(1+x)^(1//2)(1...

The value of `I=int_(-1)^(1)(1+x)^(1//2)(1-x)^(3//2)dx` is

A

`pi`

B

`(pi)/(2)`

C

`2pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int_(-1)^(1)(1+x)^(1//2)(1-x)^(3//2)dx`
`rArr" "I=int_(-1)^(1)(1-x)^(1//2)(1+x)^(3//2)dx`
`rArr" "2I=int_(-1)^(1)(1+x)^(1//2)(1-x)^(1//2)[(1-x)+(1+1)]dx`
`rArr" "2I=2int_(-1)^(1)sqrt(1-x^(2))dx`
`rArr" "I=2int_(0)^(1)sqrt(1-x^(2))dx`
`=(pi)/(2)`
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