`int_((-pi)/(2))^((pi)/(2))sin^(2)x dx`

Explanation

माना `f(x)=sin^(2)x`
`rArr" "f(-x)=[sin(-x)]^(2)=(-sinx)^(2)`
`" "=sin^(2)x=f(x)`
`rArr f(x)` एक सम फलन है ।
`therefore int_(-pi//2)^(pi//2)sin^(2)xdx=2int_(0)^(pi//2)sin^(2)xdx`
`" "=2int_(0)^(pi//2)(1-cos 2x)/(2)dx`
`" "=int_(0)^(pi//2)(1-cos 2x)dx`
`" "=[x-(sin2x)/(2)]_(0)^(pi//2)`
`" "=((pi)/(2)-(1)/(2)sin pi)-(0-0)=(pi)/(2)`