Evaluate the triple integral $$\iiint_E x\,dV$$ where $E$ is bounded by the paraboloid $x=4y^2+4z^2$ and the plane $x=4$.
I have been analyzing the part of my book where it evaluates triple integrals for paraboloids non stop, but I can't seem to figure out the method for setting it up. (and solving) I have a feeling one of the integrals will be the paraboloid given as an upper bound and the plane given as a lower bound, but I'm not sure how to get the other bounds without having to manually graph a bunch of points till i can see where everything intersects. I remember setting equations to each other to get intersections but I'm not sure how to apply that here. If someone could show me a detailed explanation of how to set this up (and solve) it would help a lot. Thanks.
I have a feeling I'm supposed to put for my outer integral $x$ is from $0$ to $4$, and my inner integrals I use the $\pm$ solutions for $y$ and $z$. Is that right? But I'm not sure how to solve it from here.