Chapter 15.9, Problem 17E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use the given transformation to evaluate the integral.

**17.** ∫∫_{R} x^{2} *dA*, where *R* is the region bounded by the ellipse 9*x*^{2} + 4*y*^{2} = 36; *x* = 2*u*, *y* = 3*v*

To determine

**To evaluate:** The integral

Explanation

**Given:**

The region *R* is bounded by the ellipse

**Property used:** Change of Variable

Change of Variable in double integral is given by,

**Formula used:**

If

**Calculation:**

Obtain the Jacobian,

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

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

Find the boundary by using the given transformation.

The ellipse

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