1. ## Intergration Probs

Hi,
Im doing Fourier Series atm for an exam on monday!

And im stuck on intergration by parts.
X cos n (pi) = ?
...........2

Im prity sure it its get broken apart into X and cos n (pi)
.................................................. ....................2

so basically what im asking is what is the integral of Cos n (pi) is it 2 Sin n (pi)
.................................................. ............................2 .................n

Sorry for the .... its the only way i could get it to line up correctly!!

thanks for your time and help

Hi,
Im doing Fourier Series atm for an exam on monday!

And im stuck on intergration by parts.
X cos n (pi) = ?
2

Im prity sure it its get broken apart into X and cos n (pi)
2

so basically what im asking is what is the integral of Cos n (pi) is it 2 Sin n (pi)
2 n

thanks for your time and help
you mean $\cos \frac {n \pi {\color {red}x}}2$, right?

choose x to be the function to differentiate and the cosine the function to integrate.

thus, $\int x \cos \frac {n \pi x}2~dx = \frac {2x}{n \pi} \sin \frac {n \pi x}2 - \frac 2{n \pi} \int \sin \frac {n \pi x}2 ~dx$

now continue

3. Originally Posted by Jhevon

thus, $- \frac 2{n \pi} \int \sin \frac {n \pi x}2 ~dx$
is the integral of this 2X -cos n(pi)X
............................n(pi).........2

sorry thanks again!

$\int \sin \frac {n \pi x}2~dx = - \frac 2{n \pi} \cos \frac {n \pi x}2$
now multiply that by the $- \frac 2{n \pi}$ and continue. note $\frac {n \pi}2$ is a constant, use substitution if you can't see the integral right away