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If agt0 and A=int(0)^(a)cos^(-1)xdx, and...

If `agt0` and `A=int_(0)^(a)cos^(-1)xdx,` and
`int_(-a)^(a)(cos^(-1)x-sin^(-1)sqrt(1-x^(2)))dx=pia-lamdaA`. Then `lamda` is

A

`0`

B

`2`

C

`3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int_(-a)^(a)(cos^(-1)x-sin^(-1)sqrt(1-x^(2)))dx`
`=int_(-a)^(0)cos^(-1)x dx +A-2 int_(0)^(a)sin^(-1)sqrt(1-x^(2))dx`
`=int_(0)^(a)(pi-cos^(-1)x)dx+A-2A`
`=api-2A` or `lamda=2`
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