   Chapter 8.2, Problem 83E

Chapter
Section
Textbook Problem

Area In Exercises 83-86, use a graphing utility to graph the region bounded by the graphs of the equations. Then find the area of the region analytically. y = 2 x e − x , y = 0 , x = 3

To determine

To calculate: The bounded region of the graph and the area of that region.

Explanation

Given: y=2xex,y=0 and x=3

Calculation:

Use Desmos calculator to draw the graph of the bounded resion.

Enter the equations as

y=2xex,y=0 and x=3

Find the area of the bounded region.

Since, y=0 then,

2xex=0xex=0

Let

x=0

Now, find the area of the bounded region with bounndry condition as x=0 and x=2.

A=02ydx

Substitute the y=2xex then,

A=022xexdx=2[xex(1)

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