I was having a looks at multiple integrals, line/surface/volume integrals and the like the other week, and decided to try some problems, but this one stumped me:
[math] \int \int_S xz\mathbf{i} + x\mathbf{j} + y\mathbf{k}\: \textrm{d} S [/math]
where S is the unit hemisphere of radius 9 for y >= 0
I thought I could change the variables to spherical co-ordinates, but I don't see how that would work with the particularly nasty stuff you'd get for the [math] \sqrt{\left( \frac{\partial z}{\partial x} \right) ^2 + \left( \frac{\partial z}{\partial y} \right) ^2 +1} [/math] along with the square roots necessary in writing z in terms of x and y.
Basically this confused the heck out of me and I'd appreciate any help
