   Chapter 6.4, Problem 23E ### 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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# Area of a Region In Exercises 21-26, find the area of the unbounded shaded region. To determine

To calculate: The area of shaded part for the provide graph: Explanation

Given Information:

The expression is provided as:

7(x1)3dx.

Formula used:

From definition of improper integral.

af(x)dx=limbabf(x)dx

Also, the expression for the integration of a polynomial is as follows:

xndx=xn+1n+1+C

Here, n0.

Calculation:

Consider the provided expression:

7(x1)3dx

For deciding the limit of integral, consider the provided graph,

From the provided graph, lower limit is and upper limit is 1 for the integration.

Use the property of improper integral af(x)dx=limbabf(x)dx and simplify as:

17(x1)3dx=lima(a17(x1)3dx)

Integrate the integrand by substation method as:

Assume x1=u

Differentiate as:

dx=du

Now, substitute the values and integrate as:

7(x1)3dx=7u3du=74u2+C

Again, substitute the value of u

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