Chapter 14.1, Problem 48E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Changing the Order of Integration In Exercises 45-50. sketch the region R of integration and change the order of integration. ∫ − 1 2 ∫ 0 e − x f ( x , y )   d y   d x

To determine

To graph: The region R of iterated integration 120exf(x,y)dydx. Further, change the order of the given iterated integration.

Explanation

Given:

The iterated integration âˆ«âˆ’12âˆ«0eâˆ’xf(x,y)dydx.

Graph:

Consider the iterated integration is âˆ«âˆ’12âˆ«0eâˆ’xf(x,y)dydx.

From the provided limits of iterated integration, it can be inferred that the inner limit of integration is

0â‰¤yâ‰¤eâˆ’x

Also, the outer limit of iterated integration is,

âˆ’1â‰¤xâ‰¤2

This means that region R is above the x-axis and below y=eâˆ’x curve. Also, the region is bounded in the interval (âˆ’1,2).

Thus, to draw the region R of given iterated integration âˆ«âˆ’12âˆ«0eâˆ’xf(x,y)dydx follow the below steps,

Step 1: Plot the graph of the curve y=eâˆ’x.

To plot y=eâˆ’x, make the following table:

xâˆ’2âˆ’1023y=eâˆ’x7.382.7110.130.05

The graph of the curve y=eâˆ’x,

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