Calculate the volume found by rotating the area between $\displaystyle x^3$ and $\displaystyle \sqrt{x}$ around y=1. I found the intersections of the two functions to be 0 and 1. I am using the slice method. Thinking of how it is outer circle-inner circle I do $\displaystyle A(x)=\pi(x^3)^2-pi(\sqrt{x})^2$. Since the line of reflection is at one of the intercepts that means I don't have to do the y intercept minus the function, I think. So then I get the formula $\displaystyle \int_0^1 A(x)$ and that gives me a negative number