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!

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- May 1st 2009, 12:16 PMbirdzIntegrate (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! - May 1st 2009, 12:24 PMReckoner
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. - May 1st 2009, 12:27 PMskeeter

integrate the last expression - May 1st 2009, 12:39 PMbirdz
Thank you for your very quick replies! I get it now :)

- May 2nd 2009, 02:07 AMMoo
It would have been better to directly note that , and then use the half angle formula (Nod)