Chapter 5: Double Integration
Section 5.2: Iterated Double Integrals
If fx,y is continuous over the rectangle R defined by a≤x≤b,c≤y≤d, its double integral over R can be evaluated by either of the two iterated integrals
∫∫Rfx,y dA = ∫ab∫cdfx,y dy dx = ∫cd∫abfx,y dx dy
There are weaker conditions under which the double integral of f can be evaluated by iteration, but in a first course in multivariate calculus, continuity suffices.
The mechanics of the iterated integral are detailed in the following examples.
If fx,y=x2+y2, and R is the square region 0≤x,y≤1, evaluate ∫∫Rf dA by both possible iterations.
If fx,y=7−3 x2−5 y2, and R is the rectangular region −1≤x≤1,−1/2≤y≤1/2, evaluate ∫∫Rf dA by both possible iterations.
If fx,y=1+5 x2+7 y2, and R is the rectangular region −1≤x≤1,−2≤y≤2, evaluate ∫∫Rf dA by both possible iterations.
<< Previous Section Table of Contents Next Section >>
© 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)