trig integrals

• Nov 8th 2009, 10:40 PM
abilitiesz
trig integrals
I just need help on one more of this type of integral:

http://img5.imageshack.us/img5/2685/mathvm.th.jpg

Can someone help me start it up? Thank you.
• Nov 8th 2009, 11:22 PM
abilitiesz
I figured it out. Thanks.
• Nov 8th 2009, 11:22 PM
simplependulum
$\frac{8}{1287}$

sub $\cos(x) = t$

$dt = - \sin(x) ~dx$

$I = \int_0^{1} t^8 ( 1 - t^2 )^2 ~dt$

$= \int_0^{1} (t^8 - 2 t^{10} + t^{12} )~dt$

$= \frac{1}{9} - \frac{2}{11} + \frac{1}{13}$

$= \frac{1}{1287} [ 143 - 234 + 99 ] = \frac{8}{1287}$