`=int_(-pi//2)^(pi//2)sin^(2)xdx` का मान है

Options

A. `(pi)/(2)`
B. `pi`
C. `(pi)/(2)+(1)/(2)`
D. `pi+1`

Answer

A

Explanation

माना `f(x)=sin^(2)x`
`f(-x)=sin^(2)(-x)=sin^(2)x=f(x)`
`thereforeint_(-pi//2)^(pi//2)sin^(2)xdx=2int_(0)^(pi//2)sin^(2)xdx`
`(2lceiling((2+1)/(2))lceiling((1)/(2)))/(2lceiling((2+0+2)/(2)))`
`=(2xx(1)/(2)sqrt(pi)xxsqrt(pi))/(2)=(pi)/(2)`