10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Area In Exercises 41-44, use partial fractions to find the area of the given region.

y = 7 16 − x 2

$Chapter 8.5, Problem 44E, Area In Exercises 41-44, use partial fractions to find the area of the given region. y=716x2$

To determine

To calculate: The area of the provided region by using partial fractions.

The graph of the region

Formula used:

1. [F(x)]ab=F(b)−F(a)

2. ∫[f(u)±g(u)]du=∫f(u)du±∫g(u)du

3. ∫1xdx=lnx+C

Calculation:

Consider the provided function.

For the above function area is given by, ∫13716−x2dx.

∫716−x2dx=7∫1(4+x)(4−x)dx

By using partial fraction method we get,

1(4+x)(4−x)=A4+x+B4−x1(4+x)(4−x)=A(4−x)+B(4+x)(4+x)(4−x)

By simplifying further, we get,

1=A(4−x)+B(4+x)

A(4−(−4))+B(4+(−4))=18A=1A=18

A(4−4)+B(4+4)=18B=1B=18

So, by substituting the value of A and B we get,

116−x2=18(4+x)+18(4−x)=18(4+x)+18(4−x)........

Check out a sample textbook solution.

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Area In Exercises 41-44, use partial fractions to find the area of the given region.

y = 7 16 − x 2

$Chapter 8.5, Problem 44E, Area In Exercises 41-44, use partial fractions to find the area of the given region. y=716x2$

Chapter 8 Solutions

Additional Math Solutions

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Calculus

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Calculus

Area In Exercises 41-44, use partial fractions to find the area of the given region. y = 7 16 − x 2

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Chapter 8 Solutions

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Math
Calculus Calculus 10th Edition

Area In Exercises 41-44, use partial fractions to find the area of the given region.

y = 7 16 − x 2

$Chapter 8.5, Problem 44E, Area In Exercises 41-44, use partial fractions to find the area of the given region. y=716x2$