# Integral of Complex exp of dot product

1. May 23, 2010

### SuperNoob

$$S(\vec{q})= \int_0^r exp(i\vec{q}\cdot\vec{x})4\pi x^2 \ dx$$

How would one approach this integral?
I tried to "ignore" the dot product and proceeded with $$exp(i\vec{q}\cdot \vec{x})=exp(iqx)$$ and got a wrong answer.

Last edited: May 23, 2010
2. May 23, 2010

### waht

If this integral is to be done in 3D, one may switch to spherical coordinates which has the volume element

$$dV = r^2 sin(\theta)\; dr\; d\theta\; d\phi$$

and also, the dot product is

$$|x||q|\; cos(\theta)$$

if x = r and play around with substitution, this integral might be easier to do.

3. May 23, 2010

Thanks!