I want to compute.

integral (integral D of y^2 sqrt x dA) where

D = {x > 0, x^2 < y < 10-x^2}

The region is basically between two parabolas. So the bounds of integration are a bit confusing.

So y would go from 10-x^2 to x^2

But I'm having a bit of trouble with x.

the parabolas intersect at sqrt 5, so what would the bounds for x be? It can go from 0 to x^2 until x reaches sqrt 5 and then back to 0 from 10-x^2.