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Find the area of the region bounded by t...

Find the area of the region bounded by the curves `y=x^2 and y = sec^-1[-sin^2x],` where [.] denotes G.I.F.

A

`pisqrt(pi)`

B

`4/3pisqrt(pi)`

C

`2/3pi(sqrt(pi)`

D

`1/3pi(sqrt(pi)`

Text Solution

Verified by Experts

The correct Answer is:
B
`[-sin^(2)x]=0` or -1 but `sec^(-1)(0)` is not defined.
`rArrsec^(-1)[-sin^(2)x]=sec^(-1)(-1)=pi`
The required area `=int_(-sqrt(pi))^(sqrt(pi))(pi-x^(2))dx=4/3pisqrt(pi)`
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