# Thread: integral problem

1. ## integral problem

Hello, can someone help me on this one, please?

integral from negative pi to pi of cos mx times cos nx dx
where m and n are positive integers.

I guess the answer is pi if m = n and zero otherwise.

Thanks!

ZD

2. Originally Posted by ZeroDivisor
Hello, can someone help me on this one, please?

integral from negative pi to pi of cos mx times cos nx dx
where m and n are positive integers.

I guess the answer is pi if m = n and zero otherwise.

Thanks!

ZD
Use the equality: $\cos(mx)\cos(nx)=\frac{1}{2}[\cos(m+n)x+\cos(m-n)x]$

3. Thank you curvature!

4. Originally Posted by curvature
Use the equality: $\cos(mx)\cos(nx)=\frac{1}{2}[\cos(m+n)x+\cos(m-n)x]$
Did you mean $\cos(mx)\cos(nx)=\frac{1}{2}[\cos((m+n)x)+\cos((m-n)x)]$ ?

5. We can use this method to find out the coefficient of cosnx in Fouriee series