Question

I am currently working with triple integrals. But I have problems figuring out the bounds of the variables.
Example question:
The solid enclosed by the cylinder x = y^2 and the planes z = 0 and x + z = 1
Evaluate this triple integral

Answer 1

hmm, x = y^2 is not a cylinder. It is a parabola. And the solid you get bycutting it with the planes is not closed. So volume would be infinite

Answer 2

My text book gives an answer though, 8/15.
I cant figure out the y and the left over x bound.

Answer 3

The bounds for z are z = 1 - x and z = 0. So the only thing left is the "double" integral for the xy-plane if you take z as a vertical axis.
But I can't figure out how to get these left over x and y bounds.

Answer 4

and that's the problem, because there are no bounds: