integration by parts with large trig functions

**gogogo** · May 15th 2010, 12:54 PM

my problem is to integrate (sin^5(x))(cos^18(x)). Lower limit is 0 and upper limit is pi/2. I tried graphing this and using calculators because my teacher didn't explain that far into using integration by parts.....

**skeeter** · May 15th 2010, 01:23 PM

Originally Posted by gogogo

my problem is to integrate (sin^5(x))(cos^18(x)). Lower limit is 0 and upper limit is pi/2. I tried graphing this and using calculators because my teacher didn't explain that far into using integration by parts.....

straight substitution will work ...

$-\int_0^{\frac{\pi}{2}} \sin^4{x} \cdot \cos^{18}{x}(-\sin{x}) \, dx$

$-\int_0^{\frac{\pi}{2}} (1-\cos^2{x})^2 \cdot \cos^{18}{x}(-\sin{x}) \, <br /> dx$

let $u = \cos{x}$

$du = -\sin{x} dx$

$-\int_1^{0} (1-u^2)^2 \cdot u^{18} \, du$

$\int_0^1 u^{18} - 2u^{20} + u^{22} \, du$

**gogogo** · May 15th 2010, 01:42 PM

wooooow! thanks!!!

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