Integral of monomials over the sphere Let
$$
I = \int_{S^2} x^iy^jz^k dx dy dz \int_{S^1} u^l v^m du dv
$$
an integral to be computed ($S^n$ being the n-sphere).
Can someone confirm me that as soon as one of the exponent $i,j,k,l,m$  is odd then $I$ is zero?

This is trivial: an odd power of a coordinate is an odd function and by symmetry the integral vanishes.
