Chapter 15, Problem 57RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use the change of variables formula and an appropriate transformation to evaluate
*R* is the square with vertices (0, 0), (1, 1), (2, 0), and (1, −1).

To determine

**To evaluate:** The integral by change of variable method.

Explanation

**Given:**

The region *R* is the square with vertices

**Property used:** Change of Variable

Change of Variable in double integral is given by,

**Calculation:**

Use the transformation *x* and *y.* Add the two transformations will yield,

Obtain the Jacobian,

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

From the given conditions, rewrite the given integral as given below.

Find the boundary by using the given transformation.

For the point

For the point

For the point

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