   Chapter 5.4, Problem 14E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Area by the Fundamental Theorem In Exercises 9-16, find the area of the region. See Example 2. y = 2 e x / 4 To determine

To calculate: The area of the region y=2ex/4 in the provided figure. Explanation

Given Information:

The function is y=2ex/4 and the provided figure is:

Formula used:

The fundamental theorem of calculus states that,

If f is integrable on interval [a,b] then abf(x)dx=F(b)F(a).

The integration formula is ekxdx=exk+C, where C, and k are the constant.

Calculation:

Consider the figure.

To find the area of the region, fundamental theorem of calculus can be used.

Integrate the function from x=0 to x=3 as shown below,

032ex/4dx

Multiply and divide by 4,

032ex/4dx=032ex/4(4)dx(4)<

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