   Chapter 15, Problem 26RE

Chapter
Section
Textbook Problem

Calculate the value of the multiple integral.26. ∬ D y   d A , where D is the region in the first quadrant that lies above the hyperbola xy = 1 and the line y = x and below the line y = 2

To determine

To calculate: The value of given double integral over the region R.

Explanation

Given:

The region D in the first quadrant lies above the hyperbola xy=1 and the line x=y and below the line y=2 .

Calculation:

Substitute x=y in xy=1 , will yield x=1 . From the given conditions, it is observed x varies from 1y to y and y varies from 1 to 2.

First, compute the integral with respect to x.

DydA=12[1yyydx]dy=12[yx]1yydy

Apply the limit value for x,

DydA=12y[y1y]dy=1<

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