   Chapter 15.3, Problem 2E

Chapter
Section
Textbook Problem

A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write ∬ R f ( x ,   y )   d A as an iterated integral, where f is an arbitrary continuous function on R.2. To determine

To write: An iterated integral by deciding whether to use polar coordinates or rectangular coordinates.

Explanation

Since the given region is a triangle, it is easier to use rectangular coordinates.

From the figure given in the problem, it is observed that x varies from 1 to 1 and y varies from x to 1.

Therefore, the rectangular coordinates is, R={(r,θ)|1x1,xy1} .

Thus the iterated integral is given by, Rf(x,y)dA=

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