Solve the integral `I=int_0^pisin^2xdx`.

Options

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

Answer

D

Explanation

`I=int_0^pisin^2xdx`
`int_0^pisin^2xdx=int_0^pi((1-cos2x)/(2))dx( :'sin^x=(1-cos2x)/(2))`
`=1/2[int_0^pidx-int_0^pi(cos2x)dx]`
`=1/2[x-(sin2x)/(2)]_0^pi`
`=1/2[(pi-0)-((sin2pi-sin0))/(2)]=pi/2`