   Chapter 5.4, Problem 6E

Chapter
Section
Textbook Problem

# The table shows values of a force function f ( x ) where x is measured in meters and f ( x ) in newtons. Use the Midpoint Rule to estimate the work done by the force in moving an object from x   =   4 to x   =   20 . x 4 6 8 10 12 14 16 18 20 f(x) 5 5.8 7.0 8.8 9.6 8.2 6.7 5.2 4.1

To determine

To estimate:

The work done by the force in moving an object from x=4 to x=20 by using  themidpoint rule

Explanation

1) Concept:

Use the midpoint rule to find the work done by considering four subintervals

2) Calculation:

With n=4, a=4 and b=20 the width of a sub-interval is

x=b-an

Substitute values,

x=20-44

x=4

And the midpoints are

x1-=12x0+x1=124+8=1212=6

x2-=12x1+x2=128+12=1220=10

x3-=12x2+x3=1212+16=1228=14

x4-=12x

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