The Area of the Surface Generated by Revolving a Graph About Any Line

Abstract

We discuss a general formula for the area of the surface that is generated by a graph $[t_0,t_1]\to {\mathbb{R}}^2$ sending $t\mapsto (x(t),y(t))$ revolved around a general line $L:Ax+By=C$. As a corollary, we obtain a formula for the area of the surface formed by revolving $y=f(x)$ around the line $y=mx+k$.

arXiv comment8 pages, 11 figures