Chapter 7.1, Problem 30E

To determine

To explain how the person A can use the data she recorded to estimate the distance between the store and her home.

Explanation of Solution

Let $R\left(t\right)$ be the rate per second at which the car travels. So, the distance between the home and the store can be found using the summation ${\displaystyle \sum R\left(t_k\right)}\Delta t$ .

Since she recorded the speed at every 10 seconds, the length of the interval can be chosen to be 10. So, $\Delta t=10$ , and $k$ is the number of subintervals.

This gives the definite integral ${\displaystyle \underset{0}{\overset{t}{\int }}R\left(t\right)dt}$ , where $t$ is the time for which the data was recorded.

This integral can be approximate using Trapezoidal rule for the obtained table of values. The value of the integral will be the distance between the home and the store.