Chapter 15.3, Problem 8E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the given integral by changing to polar coordinates.

**8.**
*R* is the region in the first quadrant enclosed by the circle *x*^{2} + *y*^{2} = 4 and the lines *x = 0* and *y = x*

To determine

**To evaluate:** The given integral by changing into the polar coordinates.

Explanation

**Given:**

The function,

The region *R* is enclosed by the circle
*.*

**Formula used:**

If
*R* given by

If

**Calculation:**

From the given region *R*, it is observed that the value of *r* varies from 0 to 2 and the value of

Substitute

Integrate the function with respect to
*r* by using the equation (2)

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