Finding volume of the solid bounded by graphs using double integral

Question

My answer is wrong and I don’t what made it wrong. Given this equations and limits: $z=x^2, x=0, x=2, y=0, y=4$ It looks like a parabola that has a plan attached to it on its right leg. As I have set up my integral which looks loke this: $\iint{x^2}dxdy$ and my limits are $x=0, x=2, y=0, y=4$ After doing the fist integral it became like this: $\int{x^3/3}dy$ Applying the limit of the x values will give me $\frac{8}{3}$ and integrating it with respect to y will give me: $\frac{8y}{3}$ Applying the limits of y and the answer will be $\frac{32}{3}$ cu. units. Is there anything that I have done wrong?