Integrate [0, 1/2] xcos(pi*x)
Every method by parts I've tried so far has turned out wrong.

Question

Integrate [0, 1/2] xcos(pi*x)
Every method by parts I've tried so far has turned out wrong.

richyw · Answer

Integration by parts should work fine. set $g=x$ and $dh=\cos(\pi x)dx$

richyw · Answer

This for sure works, I just did it. Using integration by parts and choosing what I had above.   Then just use a simple U-substitution.

anonymous · Answer

[Integrate [0, 1/2] xcos(pi*x)=(pi-2)/2(pi)^2

richyw · Answer

well yeah you can plug it into a calculator, haha. you can also plug it into wolfram. this integration is easy enough I'm almost positive it will show you the correct steps.

anonymous · Answer

[Integrate [0, 1/2] xcos(pi*x
let u=x so that du=dx
and v=intgral cos (xpi)dx
       v=(1/pi)sin(pi*x)
integration by parts
uv-itgral[0,1/2]vdu just plug ins
(1/pi)sinpi*x]-(1/pi)itgrlsin(pi*x)dx from 0 to 1/2
(1/pi)x sinpi*x - (1/pi)[-(1/pi) cos pi*x]  from 0 to 1/2
=(1/2pi)+(1/pi^2)[cos pi*x/2-cos 0]
=1/2pi  - 1/2pi^2
=(pi-2)/2pi^2  ans