Question

After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?

Options

• \[-\int(1-t^2)t^2\,dt\]

• \[-\int(1+t^2)t^2\,dt\]

• \[\int(1-t^2)t^2\,dt\]

• \[\int(1-t^2)t\,dt\]

Answer 1

Using \[\sin^2x=1-\cos^2x\] gives \[1-t^2\]. Also, \[\cos^2x=t^2\] and \[\sin x\,dx=-dt\].