Question

integrate sin^2xcos^2x dx

Answer 1

\[\int\limits_{?}^{?}\sin^2xcos^2xdx\]

Answer 2

sin^2x= 1-cos^2x/2

Answer 3

well express everything as sine or cosine
using \(cos^2x+sin^2x=1\)

Answer 4

You could also use the fact that \(\sin{2x} = 2\sin{x}\cos{x}\)

and then your integral will reduce to \(\displaystyle \int \left (\frac{\sin{2x}}{2} \right)^{2} dx\)

Now you can use the fact that \( \cos{2\theta} = 1 - 2\sin^{2}\theta\)

or alternatively \(2\sin^{2}\theta = 1 - \cos{2\theta}\) to give \(\displaystyle \int \frac{\sin^{2}{2x}}{4} dx = \int \frac{(1-\cos{4x})}{8} dx\)