Problem:

Let f(x,y,z)= xy+yz. Evaluate the triple integral of the function over the sphere centered at (1,1,1) and radius 2.

Attempted solutions:

I'm having trouble visualizing what this question is asking. So far I've done this:

1. Decided I'm probably going to use spherical coordinates given I'm working with a sphere.

2. Converted the integral to spherical coordinates.

Questions:

1. How do I go about describing the given sphere in spherical coordinates? I know how to describe the unit sphere, but I can't figure out how to describe spheres that have been transformed (such as this one).

2. Am I finding the volume beneath xy+yz bounded below by the sphere?

Any other tips would be great! Thanks.