I want to set up an integral that can get the volume surrounded by $y=x^2$, $x=1$, and $y=0$ revolved about the line $y=-10$.
This is what I have so far: $$\int\limits\limits_{0}^{1} 2 \pi \ (10-y)(\sqrt{y})\ dy$$
But I have not been able to get a correct answer out of this integral.