   Chapter 8.7, Problem 64E

Chapter
Section
Textbook Problem

Area In Exercises 63 and 64, find the area of the region bounded by the graphs of the equations. y = x 1 + e x 2 ,   y = 0 ,   x = 2

To determine

To calculate: The area of the region bounded by the graphs of the equations y=x1+ex2,y=0 and x=2.

Explanation

Given:

y=x1+ex2,y=0 and x=2

Formula used:

The area of a region from x=a to x=b:

abf(x)dx

The integration formula,

11+eudu=uln(1+eu)

Calculation:

Consider the equations,

y=x1+ex2,y=0 and x=2

Now, determine the coordinate points for the function y=x1+ex2 as shown below in the table.

 Values of x Values of y Coordinate points 0 0 (0,0) 0.5 0.218 (0.5,0.218) 1 0.268 (1,0.268) 1.5 0.143 (1

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