Need help commputing double integral and volume

Hello, I am doing the practice problems for my last lecture and I don't think these types of questions were covered even though I think they were supposed to be... Could you please help.

1) Find the volume of the solid under z=1-y^{2} and above z=x^{2}...

2) Find the volume inside the cylinder x^{2} + 2y^{2} = 8, above the plane z=y-4, and below the plane z=8-x...

Any help is really appreciated.

Re: Need help commputing double integral and volume

Hey lytwynk.

Hint: The first thing you have to do is find the region that these two objects intersect. Can you find them?

Re: Need help commputing double integral and volume

For 1) wont they intersect where x^2+y^2 =1? And for 2) im not really sure...

Re: Need help commputing double integral and volume

Hello, I am still having troubles. I can't find the region that these objects intersect in. For question one I think they will intersect over a rectangle that I think will have an cross section area of 4y*sqrt(1-y^2) but then I am having trouble integrating it. Is this even right? I really have no clue how to do this stuff.