Find the area of the region bounded by the curve `y=x^2` and `y=sec^(-1)[-sin^(2)x]`, where [.] denotes the greatest integer function.

Options

A. `pisqrt(pi)`
B. `4/3pisqrt(pi)`
C. `2/3pi(sqrt(pi)`
D. `1/3pi(sqrt(pi)`

Answer

B

Explanation

`[-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)`