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 [itex]d=2-\epsilon[/itex] dimension to regularize my integral. Now, suppose [itex]\theta[/itex] 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!