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

#### superdude

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(Doh)

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#### matheagle

MHF Hall of Honor
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.

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