use integration by parts to find:

$\displaystyle \int^{\frac{\pi}{2}}_{0} xsin^2xcosx dx$

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- Mar 22nd 2009, 04:39 PMqznointegration by parts
use integration by parts to find:

$\displaystyle \int^{\frac{\pi}{2}}_{0} xsin^2xcosx dx$ - Mar 22nd 2009, 05:05 PMskeeter
$\displaystyle u = x$

$\displaystyle du = dx$

$\displaystyle dv = \sin^2{x}\cos{x} \, dx$

$\displaystyle v = \frac{\sin^3{x}}{3}$

$\displaystyle \int x\sin^2{x}\cos{x} \, dx = \frac{x\sin^3{x}}{3} - \int \frac{\sin^3{x}}{3} \, dx$

for the last integral ...

$\displaystyle \sin^3{x} = (1 - \cos^2{x})\sin{x} = \sin{x} + \cos^2{x}(-\sin{x})$ - Mar 22nd 2009, 05:07 PMqzno
$\displaystyle dv = \sin^2{x}\cos{x} \, dx$

$\displaystyle v = \frac{\sin^3{x}}{3}$

is this a rule? - Mar 22nd 2009, 05:22 PMskeeter