   Chapter 15, Problem 9RE

Chapter
Section
Textbook Problem

Write ∬ R f ( x ,   y )   d A as an iterated integral, where R is the region shown and f is an arbitrary continuous function on R. To determine

To write: The integral Rf(x,y)dA as an iterated integral.

Explanation

Calculation:

From the given figure, it is observed that the given portion is an annular region with two circles of radius 2 and 4. Since, the annular region is given, use of polar coordinates is more appropriate to use with. From the given figure, it is observed that r varies from 2 to 4 and θ varies from 0 to 2π . Substitute x=rcosθ,y=rsinθ . Thus, by the equation (1), the required integral is given by, Rf(x,y)dA=0π

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