1. The problem statement, all variables and given/known data Find the volume of the solid region E bounded by the paraboloids z = 1+x^2+y^2 and z = 4 - 2x^2 - 11y^2 3. The attempt at a solution i set up a triple integral using Cartesian coordinates but was unable to solve it because the limits of integration where very hard to integrate, i don't think you can use cylindrical coordinates because the intersection is an eclipse: x^2 + 4y^2 = 1. PLease somebody show me a good method to do this question as it was in a past exam and might come up again. Please help me. thanks.