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1. Evaluate the double integral of x+ 2y whose region of integration is represented below. y =1 16 =1+x² 2x

1. Evaluate the double integral of x+ 2y whose region of integration is represented below. y =1 16 =1+x² 2x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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21:54 ul 4G O 11. Evaluate the double integral of x+ 2y whose region of integration is represented below. y =1+x| 16 =1+x² 2x Add a caption... > Status (Custom) +
Transcribed Image Text:21:54 ul 4G O 11. Evaluate the double integral of x+ 2y whose region of integration is represented below. y =1+x| 16 =1+x² 2x Add a caption... > Status (Custom) +
Expert Solution
Step 1

Consider a function f(x, y) defined at every point of the 2-dimensional finite region A Divide A into n elementary areas dA1, dA2, dA3, ···, dAn. Let (a, b) be any point within the rth sub-division dAr. Consider the sum

∑r=1∞fa, bdAr

The limit of the sum, if it exists, as n→∞ and dAr→0 is called the double integral of f(x, y) over the region A denoted by

∫∫fx, ydxdy

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