   Chapter 8.2, Problem 84E

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 = 1 10 x e 3 x ,   y = 0 ,   x = 0 ,   x = 2

To determine

To Calculate: The area of the region bounded by the equations and also plot the graph of the bounded region

Explanation

Given:given equations are y=110xe3x,y=0,x=0 and x=2

Graph:

By Using ti-83 calculator to draw the graph of the bounded region.

We are using the steps given below:

Step 1: Firstly, Press (y=) key.

Step 2: Then, enter the equation.

Step 3: Press 2nd key and then press Trace key.

Step 4: Finally, Press 7th key.

Step 5: after step 4, enter lower limit and then press enter key.

Step 6: similarly, enter upper limit and then press enter key.

The required graph is shown below,

Calculation:

To Find the area of the bounded region by the equations y=xe3x,y=0,x=0 and x=2.

Now, in order to find the area of the bounded region by x=0 and x=2

We have,

A=02ydx

Now, Substitute y=xe3x then,

On calculating,

A=02xe3xdx=[xe3x31×e3x(3

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