# How to do this integral ?

1. May 21, 2014

### hiyok

Hi,

I'm stumbled on the following integral,

$\int d\vec{q} e^{i\vec{q}\vec{r}} \cos(2\theta)$,

where $\theta$ denotes the angle of the vector $\vec{q}$ and the $\vec{r}$ is an arbitrary vector. The integral domain is a circular area of radius $D$.

Could anyone help me out ?

Many thanks.

hiyok

2. May 21, 2014

### mathman

Try cos(2θ) =(exp(2iθ)+exp(-2iθ))/2

3. May 21, 2014

### hiyok

I have worked it out. It amounts to zero by symmetry.

4. May 24, 2014

### amind

5. May 24, 2014

### eigenperson

If you're going to ignore both the original poster's notation ($\theta$ has a specific meaning, and it's a vector integral) and the domain of integration, you can't expect to just type the integral into Wolfram Alpha and expect to get the right result.

6. May 24, 2014

### amind

I'm sorry for that , I'm not great in calculus and I probably skimmed through the posts.
:(