Chapter 15.9, Problem 28E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Let *f* be continuous oil [0, 1] and let *R* be the triangular region with vertices (0, 0), (1, 0), and (0, 1). Show that
*x* + *y*) *dA* =

To determine

**To show:** The integral

Explanation

**Given:**

The function *f* is continuous on *R* be the region with vertices

**Property used:** Change of Variable

Change of Variable in double integral is given by,

**Proof:**

Let

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 given region in

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