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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.4, Problem 15E
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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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Finding Area by the Fundamental Theorem In Exercises 9-16, find the area of the region. See Example 2.

y = x 2 + 4 x

Chapter 5.4, Problem 15E, Finding Area by the Fundamental Theorem In Exercises 9-16, find the area of the region. See Example

To determine

To calculate: The area of the region y=x2+4x in the provided figure.

Calculus: An Applied Approach (MindTap Course List), Chapter 5.4, Problem 15E

Explanation

Given Information:

The function is y=x2+4x 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 ∫xndx=xn+1n+1+C and ∫1xdx=lnx+C

Calculation:

Consider the figure.

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

Integrate the function from x=1 to x=4 as shown below.

∫14(x2+4x)dx

This can be written as,

∫14(x2+4x

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