Chapter 15.9, Problem 23E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the integral by making an appropriate change of variables.

**23.**
*dA.* Where *R* is the parallelogram enclosed by the lines *x* – 2*y* = 0, *x* – 2*y* = 4, 3*x* – *y* = 1, and 3*x* – *y* = 8

To determine

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

Explanation

**Given:**

The integral is

**Property used:** Change of Variable

Change of Variable in double integral is given by,

**Definition used:** Jacobian transformation

**Formula used:**

If

**Calculation:**

Let

Obtain the value of

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

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