I need to find the volume of the cylinderical column standing on the area common to parabola $y= x^2$ and $x =y^2$ as base and cutoff by the surface $z= 1+y-x^2$.
So I set up the integral as :
Volume = $\displaystyle\int_0^1\int_{x^2}^{\sqrt{x}} \int _0 ^{1+y-x^2}dzdydx$
My question is : Is this setup correct ?