Chapter 6: Applications of Double Integration
Section 6.3: Surface Area
Example 6.3.3
Calculate the surface area of the surface defined by the function whose domain is the plane region , the region bounded by the graphs of and on .
See Example 6.2.3.
Solution
Mathematical Solution
The surface is , so the surface-area element is
The surface area is then given by the iterated integral
=
Because , the integral can be evaluated in closed form.
Maple Solution - Interactive
Table 6.3.3(a) contains a solution from first principles.
Initialize
Context Panel: Assign Name
Obtain
Expression palette: Square-root template
Calculus palette: Partial derivative template
Context Panel: Evaluate and Display Inline
Write and evaluate the relevant iterated integral
Calculus palette: Template for iterated double integral
Table 6.3.3(a) Solution from first principles
Maple Solution - Coded
Install the Student MultivariateCalculus package.
Define the surface.
Apply the SurfaceArea command from the Student MultivariateCalculus package
Because , the surface integral can be evaluated in closed form.
A solution from first principles must necessarily begin with the calculation of
The top-level Int command returns the inert iterated integral
<< Previous Example Section 6.3 Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2024. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document