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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Area of a Region In Exercises 21-26, find the area of the unbounded shaded region.

y = e x

Chapter 6.4, Problem 21E, Area of a Region In Exercises 21-26, find the area of the unbounded shaded region. y=ex

To determine

To calculate: The area of the unbounded shaded region for the function y=ex.

Calculus: An Applied Approach (MindTap Course List), Chapter 6.4, Problem 21E

Explanation

Given Information:

The provided function is, y=ex and the graph is:

Formula used:

The area between two graphs:

If f(x)g(x) for all x in [a,b] (so that the graph of f doesn’t move below that of g), then the area of the region between the graphs of f and g and between x=a and x=b is given by:

A=ab[f(x)g(x)dx]

From definition of improper integral.

af(x)dx=limbabf(x)dx

Also, the expression for the integration of an exponential is as follows:

eaxdx=eaxa+C; where a0.

Calculation:

Here, the two functions are f(x)=ex and g(x)=0 and the graph is going from 0 to 

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