Help with calculating volume with double integrals

[frMoy]

So, the exercise goes like this: calculate the volume of the determined solid below the paraboloid z = x^2 + y^2 and above the region bounded by y = x^2 and x = y^2 - y.
Im having trouble establishing the intersection points of the two functions of the region.
Thanks in advance.

 

[Steven G]

In order to receive help on this site you will need to post the work that you have done so far. We do not solve problems for students here but rather we help students solve their own problem.

Since you are having trouble finding intersecting points you then have work to show us. So please post back.

 

[Dr.Peterson]

So, the exercise goes like this: calculate the volume of the determined solid below the paraboloid z = x^2 + y^2 and above the region bounded by y = x^2 and x = y^2 - y.
Im having trouble establishing the intersection points of the two functions of the region.
Thanks in advance.

I presume you're specifically having trouble finding the intersection of y = x^2 and x = y^2 - y. That is indeed difficult, as substitution leads to a 4th degree equation with one obvious root, but no other rational roots. It can be solved, but the results aren't pretty.

My first thought would be to check that you copied the problem correctly, and that there are no hints or other information supplied. This sort of thing can happen in real life, but in a class exercise, I expect to be able to find exact results without excessive effort.

Maybe you should show us an image of the actual problem.