# Integral of angular functions over d-dim solid angle

1. Nov 18, 2015

### Einj

Hello everyone! I have a question about angular integration in arbitrary d dimensions. The interest comes from the need to use dimensional regularization. Suppose I start with a 2-dimensional integral and then I have to move to $d=2-\epsilon$ dimension to regularize my integral. Now, suppose $\theta$ is the polar angle in the original 2 dimensions and now I want to compute the following integrals:

$$\int d\Omega_d\cos\theta ,$$
$$\int d\Omega_d\cos^2\theta.$$

What is the result? Can I still say that the first integral is zero? What about the second?

Thanks a lot!

2. Nov 23, 2015