Originally Posted by

**jackie** My friend and I ran into another problem that we were not able to solve. If anyone can gives us a hint, we'd really appreciate it.

A solid is generated by **rotating the curve** $\displaystyle y=f(x)$ where $\displaystyle 0\leqslant x \leqslant c$ **about the x-axis**, and the resulting volume is $\displaystyle c^2 + c$. We want to find the function $\displaystyle f(x)$.

We have the volume using disk method $\displaystyle V=\int_0^c \pi r^2 dx=c^2+c$. But $\displaystyle r=y=f(x)$, and I don't know how to change the variable of the expression inside the integral so that I can integrate it.