Here is the problem in my textbook:
Find the volume of the solid obtained by rotating the region bounded by the curves $y=x, y=x^2$ about x-axis.
Here is my solution :
Because equation $x = x^2$ has two roots : $0$ and $1$. we have:
$ V= \int_0^1{2\pi x(x^2-x)}dx = \frac{\pi}{6}$
But the solution in my textbook is $\frac{2\pi}{15}$. I think the hole in my solution is : I haven't use the region rotate around x-axis
yet. But, I don't know how to use this statement in solution when couting volume.
Thanks :)