# Thread: find volume created by rotating area between 2 curves around line

1. ## find volume created by rotating area between 2 curves around line

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

2. It haven't done one of these in over 10 years.
It's important to draw AND note which line you're revolving about.

The formula I believe is $\displaystyle \pi\int_0^1 (R^2-r^2)dx$.

And by looking at the picture, each radius is 1-y.

So $\displaystyle R=1-x^3$ is the outer radius and the smaller radius is $\displaystyle R=1-\sqrt x$.

Hopefully this leads to a postive volume.