I'm trying to find the volume of the region enclosed by the curves above, rotated along the x-axis. I know how to do this if $x\ge0$ but with this there are two regions, and I'm not sure how to handle that.
For example, if I find the intersections to find x: $$x^3=x\rightarrow x^3-x=0 \rightarrow x(x^2-x)=0\rightarrow x=\pm1 \;and\;x=0$$ So, I have three x's and I do not know how to set up the integration part of the problem.
Thanks for any help!
Best Answer
Just calculate $$2\pi\int\limits_{0}^1(x^2-x^6)dx$$