   Chapter 5.4, Problem 13E ### 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 = 3 e − x / 2 To determine

To calculate: The area of the region y=3ex/2 in the provided figure. Explanation

Given Information:

The function is y=3ex/2 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 exdx=ex+C.

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=0 as shown below,

043ex/2dx

Multiply and divide by (2),

043ex/2dx=043ex/2(2)dx(2)

Now find antiderivative by applying the integration formula,

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