   Chapter 4, Problem 73RE

Chapter
Section
Textbook Problem

Finding the Area of a Region In Exercises 73 and 74, find the area of the region. Use a graphing utility to verify your result ∫ 1 9 x x − 1 3   d x To determine

To calculate: The value of the integral 19xx13dx that gives the area of the shaded region: Explanation

Given:

The integral 19xx13dx.

Formula Used:

The area below the curve y=f(x) and above the x-axis when x lies in the interval [a,b] is given by:

A=abf(x)dx

Calculation:

Define the following variable:

x1=udx=du

When x=1,u=0 and when x=9,u=8.

Use this to rewrite the integral as:

19xx13dx=08(u+1)u13du

Now, thus can be evaluated as:

08(u+1)

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