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Area of region bounded by the curve y=(1...

Area of region bounded by the curve `y=(16-x^(2))/(4)` and `y=sec^(-1)[-sin^(2)x]` (where [x] denotes the greatest ingeger function) is

A

`pi sqrt pi `

B

`4/3 pi sqrt pi `

C

`2/3 pi sqrt pi `

D

`1/3 pi sqrt pi `

Text Solution

Verified by Experts

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