Chapter 15.9, Problem 25E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the integral by making an appropriate change of variables.

25.
*dA*, where *R* is the trapezoidal region with vertices (1, 0), (2, 0), (0, 2), and (0, 1)

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

**Calculation:**

From the given integral observe and let

Obtain the value of

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

Substitute the corresponding values in equation (2),

This is in the form of inverse of Jacobian transformation

Substitute the given vertices of trapezoidal in

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