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

Edray Herber Goins; Talitha M. Washington

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

History and Overview 2011-08-15 v1 Metric Geometry

Authors: Edray Herber Goins , Talitha M. Washington

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 $t \mapsto \bigl(x(t), y(t) \bigr)$ 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 $y = m x + k$ .

Keywords

surface area revolution general line parametric curve calculus

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@article{arxiv.1108.2624,
  title  = {The Area of the Surface Generated by Revolving a Graph About Any Line},
  author = {Edray Herber Goins and Talitha M. Washington},
  journal= {arXiv preprint arXiv:1108.2624},
  year   = {2011}
}

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8 pages, 11 figures

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

Abstract

Keywords

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