   Chapter 15.2, Problem 48E

Chapter
Section
Textbook Problem

Sketch the region of integration and change the order of integration. ∫ − 2 2 ∫ 0 4 − y 2 f ( x ,   y )   d x   d y

To determine

To sketch: The outline of the region of integration and change the order.

Explanation

Given:

The region D is enclosed by the plane y = 0 and the circle x2+y2=4 .

Calculation:

From the given conditions, x varies from 0 to 4y2 and y varies from −2 to 2. Use these values and sketch the graph as given below in the Figure 1.

From Figure 1, it is observed that y varies from 4x2 to 4x2 and x varies from 0 to 2.

2204y2

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