This question stumped me on a recent calculus test... I would really like an explanation.
The region $\mathbf{R}$ is bounded by
\begin{equation*} h(x) = -0.8(x-2)^2 + 8~\text{and}~p(x) = x\cos(x) - \ln(2x+2). \end{equation*}
Find the lateral surface area of the solid formed when $\mathbf{R}$ is revolved around the line $y=11$.
I tried to convert both functions into terms of y so that I could get the arc length, but that didn't get me very far. Any help would be greatly appreciated.