Efficient Integration Strategies for Solving Fourier Series Problems

[dvchench]

I'm doing a HW problem that involved trying to find Fourier series. I know how to do it, but I'm really bothered by the fact that I have to do so much trigonometric integration by parts. my question is, is there any better way to solve the problem:

<int,indef.,dt>{ sin(a*t)*cos(b*t) } or is the only way to chug along with the two messy layers of integration by parts?

also, it seems like I'm missing something: how do you write pretty-print equations in posts?

edit: i should add, that the problem is asking for a Fourier series for a half-wave rectified sine, but that isn't vital to the question

 

[gabbagabbahey]

I'm doing a HW problem that involved trying to find Fourier series. I know how to do it, but I'm really bothered by the fact that I have to do so much trigonometric integration by parts. my question is, is there any better way to solve the problem:

<int,indef.,dt>{ sin(a*t)*cos(b*t) } or is the only way to chug along with the two messy layers of integration by parts?

Why are you concerned with the indefinite integral? Usually one integrates over a half-period interval in order to take advantage of the orthogonality of sine and cosine.

also, it seems like I'm missing something: how do you write pretty-print equations in posts?

See my signature.

 

[dvchench]

gabbagabbahey,
thanks for the reply. I'm only concerned because it seems like I'm doing it the hard way - after 1.5 pages of math, I'm starting to feel like I'm mowing the lawn with a pair of nail clippers (or mopping a gym floor with a toothbrush, take your pick of metaphor). I just wanted to make sure that by parts is the only reasonable way of doing it and I'm not missing any good shortcut.

 

[dvchench]

so i found the answer here: https://www.physicsforums.com/showthread.php?t=98825

maybe my wording of this question wasnt good enough. o well.