Evaluate the triple integral ∭E(x+3y)dV where E is bounded by the parabolic cylinder y=6x2 and the planes z=4x,y=12x, and z=0.

Answer 1

The only difficulty is setting up the limits of integration where the most outer integral will have constants according to a chosen variable, then the middle and inner integral will have as limits functions of that preordained variable.

This video with 3 d drawing will explain how the limits are chosen.

It will post shortly.