Thread: Integrate (sin(x))^2(cos(x))^2

As the title says, I need help with Integrate (sin(x))^2(cos(x))^2

I get thet I need to use the half- angle formula, but do I use it on both sin(x)^2 and cos(x)^2? And where do I go from there. Much appreciated!

Originally Posted by birdz

As the title says, I need help with Integrate (sin(x))^2(cos(x))^2

I get thet I need to use the half- angle formula, but do I use it on both sin(x)^2 and cos(x)^2? And where do I go from there. Much appreciated!

If you use the half-angle/power reduction formula on both factors from the start, you can then expand and use the formula again.

Alternatively, you could first use the Pythagorean identity, to get everything into terms of either sine or cosine. Then you could apply the half-angle formula twice. I don't think this would be any easier, but it is certainly valid.

integrate the last expression

Thank you for your very quick replies! I get it now

It would have been better to directly note that , and then use the half angle formula