   Chapter 4.1, Problem 13E

Chapter
Section
Textbook Problem

# The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v(ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2

To determine

To find:

The lower and upper estimates for the distance

Explanation

1) Concept:

The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles

A=limni=1nfxix

where,

x=b-an & xi=a+ix

2) Calculation:

Lower estimate for the distance is

L=0.5(0+6

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