Area bounded by the curve `y=sin^(2)x` and lines `x=(pi)/(2),x=pi` and X-axis is

Options

A. `(pi)/(2)` sq unit
B. `(pi)/(4)` sq unit
C. `(pi)/(8)` sq unit
D. None of these

Answer

B

Explanation

Required area
`A=int_(pi//2)^(pi)sin^(2)xdx`
`=(1)/(2)int_(pi//2)^(pi)(1-cos2x)dx`
`=(1)/(2)[x-(sin2x)/(2)]_(pi//2)^(pi)=(pi)/(4)` sq unit