Find the mass of the first orthant $(x, y, z ≥ 0)$ surface of the 3D sphere with a point density of $δ(x,y,z) = xyz$ using a surface integral.
I started by integrating with respect to dA, doing the double integral $$I = \iint δ(x,y,z) dA$$. I'd like to convert this into something I can actually integrate, but I don't know what conversion I would use (maybe polar?). I think it has something to do with a Jacboian matrix, but I'm unclear how to do such.
All help and input appreciated.