Chapter 7: Triple Integration
Section 7.1: The Triple Integral
In Maple, implement the definition of the triple integral for fx,y,z=1+2 x+3 y+5 z on the region R defined by the inequalities 1≤x,y,z≤2.
Define fx,y,z as the integrand
Context Panel: Assign Function
fx,y,z=1+2 x+3 y+5 z→assign as functionf
Form a Riemann sum
Expression palette: Summation template
Context Panel: Assign Name
q=∑i=1u∑j=1v∑k=1wf1+iu,1+jv,1+kw⋅1u v w→assign
Obtain an iterated limit
Apply the relevant form of the limit command.
limitq,u=∞,v=∞,w=∞ = 16
In three dimensions, Maple's limit command computes iterated limits, not a true multidimensional limit. This is in distinction to the two-dimensional case where, for certain functions, Maple can obtain a true bivariate limit. Note also that there is no convenient "syntax-free" way to implement the multidimensional limit.
The expression for the Riemann sum in three dimensions can be cumbersome. Its simplified form is displayed below.
simplifyq = 12⁢32⁢u⁢v⁢w+5⁢u⁢v+3⁢u⁢w+2⁢v⁢ww⁢u⁢v
<< Previous Example Section 7.1
Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2021. 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
What kind of issue would you like to report? (Optional)