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

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

2011-08-02

arxiv.org/abs/1108.2624v1

Mathematics

History and Overview

8 pages, 11 figures

Scientific paper

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 $t \mapsto \bigl(x(t), y(t)
\bigr)$ revolved around a general line $L: A x + B y = C$. As a corollary, we
obtain a formula for the area of the surface formed by revolving $y = f(x)$
around the line $y = m x + k$.

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