1. ## Trigonometric Integration Question

Hi, just a quick question.

Doing a bit of Fourier Series and I've come across this integral, is there a best way to go about doing this?

$\frac{2}{\pi} \int_0^{\pi} \cos{(x)} \sin{(nx)} dx$, where $n$ is an integer $0 \leq n \leq \infty$.

I've attempted by using the product to sum formulas, but this just ends up with at least two sides of tricky algebra.

Has anyone come across this before, or have any helpful 'shortcuts'?

2. What do you mean with trick algebra?
It is easy.
All what you need is : $sin(A)cos(B)=\dfrac{1}{2} \left( sin(A-B) + sin(A+B) \right)$

3. Originally Posted by Liverpool
What do you mean with trick algebra?
It is easy.
All what you need is : $sin(A)cos(B)=\dfrac{1}{2} \left( sin(A-B) + sin(A+B) \right)$
Ohh sorry, meant tricky algebra.

I've sort of done it with the product to sum formulas, was just wondering if anyone know of a shorter way.

4. Originally Posted by craig
Ohh sorry, meant tricky algebra.

I've sort of done it with the product to sum formulas, was just wondering if anyone know of a shorter way.
That IS the shortest way...

5. Ahh thought as much, merci