   Chapter 14.1, Problem 48E

Chapter
Section
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 120exf(x,y)dydx.

Graph:

Consider the iterated integration is 120exf(x,y)dydx.

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

0yex

Also, the outer limit of iterated integration is,

1x2

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

Thus, to draw the region R of given iterated integration 120exf(x,y)dydx follow the below steps,

Step 1: Plot the graph of the curve y=ex.

To plot y=ex, make the following table:

x21023y=ex7.382.7110.130.05

The graph of the curve y=ex,

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