Question

PLEASE HELP:
Express the integral as an iterated integral in six different ways, where E is the solid bounded by the given surfaces y=4-x^2-4z^2 , y=0

Answer 1

The six different ways are going to be:
dxdydz
dxdzdy
dydxdz
dydzdx
dzdxdy
dzdydx

Answer 2

But you have to find the bounds such that you can integrate in these orders.

Answer 3

Okay. so the easiest boundary to start with is when you integrate with respect to y first.

Answer 4

This this sort of parabaloid which I drew poorly.