# Surface integral

Problem : Evaluate [double integral]f.n ds where f=xi+yj-2zk and S is the surface of the sphere x^2+y^2+z^2=a^2 above x-y plane.

My effort:: I know that the sphere's orthogonal projection has to be taken on the x-y plane,but I'm having trouble with the integration.Please help!

Galileo
Homework Helper
Calculating flux integrals can be a bit tedious. Although some are very easy when you invoke the right theorem. Like this one.

mjsd
Homework Helper
Problem : Evaluate [double integral]f.n ds where f=xi+yj-2zk and S is the surface of the sphere x^2+y^2+z^2=a^2 above x-y plane.

My effort:: I know that the sphere's orthogonal projection has to be taken on the x-y plane,but I'm having trouble with the integration.Please help!

you want to find f.n where n is obviously the normal to the surface .. find that first... the easiest way to do this is probably change to spherical coordinates...given the symmetry of the problem

HallsofIvy
Or you can use the "Divergence theorem" and integrate $\nabla \cdot f$ over the interior of the sphere, as Galileo suggested. Here $\nabla \cdot f$ is particularly simple.