Today was my test and I've absolutely no idea about if I'll pass it or not. (On the cut, or I don't know how to say)

I had to calculate the volume between the paraboloids

and

, if I remember well.

I've thought about it and I think that using Cartesian coordinates will be easier than spherical and cylindrical ones.

However I tried to calculate the volume via cylindrical coordinates:

. I tried to set up the triple integral :

goes from

to

.

from

to

.

And

goes from

to .... I wasn't sure. But I strongly believe I already made an error.

I have 2 questions : How can I calculate the volume they ask using cylindrical coordinates?

With what method would you solve the problem?

Thank you very much!

Oh, and before I forget, I know they cross each other with a circular (

) section.