   Chapter 8.5, Problem 44E

Chapter
Section
Textbook Problem

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

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

Explanation

Given:

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.

y=716x2

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

Now,

716x2dx=71(4+x)(4x)dx

By using partial fraction method we get,

1(4+x)(4x)=A4+x+B4x1(4+x)(4x)=A(4x)+B(4+x)(4+x)(4x)

By simplifying further, we get,

1=A(4x)+B(4+x)

.At x=4,

A(4(4))+B(4+(4))=18A=1A=18

At x=4,

A(44)+B(4+4)=18B=1B=18

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

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

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