Chapter 15.9, Problem 20E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use the given transformation to evaluate the integral.

**20.** ∫∫_{R} y^{2} *d*A, where *R* is the region bounded by the curves *xy* = 1, *xy* = 2, *xy*^{2} = 2; *u* = *xy*, *v* = *xy*^{2}. Illustrate by using a graphing calculator or computer to draw *R*.

To determine

**To evaluate:** The integral

Explanation

**Given:**

The region *R* bounded by the curves

**Property used:** Change of Variable

Change of Variable in double integral is given by,

**Formula used:**

If

**Calculation:**

Obtain the Jacobian,

Write *u* and *v* in terms of *x* and *y* respectively.

Find the partial derivative of *x* and *y* with respect to *u* and *v.*

From the given integral the function is,
*x* and *y*

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