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given integral over the specified region. image. where D is the ri

given integral over the specified region. image. where D is the ri

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 97E
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Find the given integral over the specified region.

image.

where D is the ring 1 ≤ x2  + y2  ≤ 4

2.2 dA (x² + y?)²
Transcribed Image Text:2.2 dA (x² + y?)²
Expert Solution
Step 1

Introduction:

The volume under the surface z=f(x,y) over a region D can be interpreted as the integral of a function f(x,y) over a region D. As we did previously, we can try integrating the function f(x,y)=1 over the region D. This would give the volume under the f(x,y)=1 function over D. The integral of f(x,y)=1 is, however, also the area of the region D. This is a useful method for calculating the area of the region D. We can write this as A=∬DdA if A is the area of the region D.

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