Surface of Revolution - Maple Programming Help

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Home : Support : Online Help : Tasks : Calculus - Integral : Applications : Solids of Revolution : Task/SurfaceOfRevUnivariateFcn

Surface of Revolution

 Description Calculate the surface area of a surface of revolution generated by rotating a univariate function about the horizontal or vertical axis.

Enter the function as an expression and specify the range:

 >
 ${\mathrm{sin}}{}\left({x}\right){,}{0}{..}{\mathrm{π}}$ (1)

Calculate the surface of revolution:

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{SurfaceOfRevolution}\right]\left(\right)$
 ${2}{}{\mathrm{π}}{}\sqrt{{2}}{+}{2}{}{\mathrm{π}}{}{\mathrm{ln}}{}\left({1}{+}\sqrt{{2}}\right)$ (2)

Display the floating-point value using the evalf command:

 > $\mathrm{evalf}\left(\right)$
 ${14.42359945}$ (3)

Display a plot using the output = plot option:

 >

Display the exact solution (integral form) using the output = integral option:

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{SurfaceOfRevolution}\right]\left(,\mathrm{output}=\mathrm{integral}\right)$
 ${{∫}}_{{0}}^{{\mathrm{π}}}{2}{}{\mathrm{π}}{}{\mathrm{sin}}{}\left({x}\right){}\sqrt{{1}{+}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (4)

Alternatively, you can use the Surface of Revolution tutor, a point and click interface.  You can launch the tutor in two ways:

 • From the Tools menu, select Tutors, Calculus - Single Variable, and then Surface of Revolution.
 • Use the following command to launch the tutor:

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{SurfaceOfRevolutionTutor}\right]\left(\right)$
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