messy integral (?)

**nmanik90** · February 9th 2008, 01:20 PM

could somebody help me integrate the following please:

(sin x)^4 (cos x)^5 dx

(the limits are pi/2 and 0 but i can solve that once the initial integration has been done)

im not sure how to split it up to make it easier, because when i do use trig identities it becomes very messy....

cheers

**Krizalid** · February 9th 2008, 01:37 PM

$\int_0^{\pi /2} {\sin ^4 x\cos ^5 x\,dx} = \int_0^{\pi /2} {\sin ^4 x\left( {\cos ^2 x} \right)^2 \cos x\,dx} .$

Since you know that $\cos^2x=1-\sin^2x,$ you just replace it and make the obvious substitution. (Don't forget to get the new integration limits for your new variable.)

**mr fantastic** · February 9th 2008, 01:38 PM

Originally Posted by nmanik90

could somebody help me integrate the following please:

(sin x)^4 (cos x)^5 dx

(the limits are pi/2 and 0 but i can solve that once the initial integration has been done)

im not sure how to split it up to make it easier, because when i do use trig identities it becomes very messy....

cheers