Question

Use Gauss’s theorem to find the volume of the solid region bounded by the paraboloids z=9−x^2−y^2 and z=3x^2+3y^2−16.

Answer 1

Gauss is theorem is also Divegence theorem, I believe. Which says:

Let E be a simple solid region and S is te boundry surface of E with the positive orientation. Let f be a fector field whose components have cintinuous first order partial deriv. Then:
\[\int\limits \int\limits_{S }^{ } F • dS = \int\limits \int\limits_{E }^{ } \int\limits dive F dV\]

Answer 2

where F is a vector.

Answer 3

So, I think you want to start by getting the divergence of the vector field firest.

Answer 4

How do I find the vector field, if all im given is equations for parabaloids?