We did not spend a lot of time in class on Riemann sum so I confused with this question.
Speedometer readings for a motorcycle at $12$-second intervals are given in the table below.
$$ \begin{array}{c|c|c|c|c} t sec & 0 & 12 & 24 & 36 & 48 & 60 \\ \hline v(t) ft/sec & 23 & 22 & 18 & 17 & 20 &23\\ \end{array} $$
Estimate the total distance traveled during the time interval $[0,60]$ using a Riemann sum based on the table data.
I hope someone can help. Thanks.
The definition of a Riemann sum is as following:
Let $f$ be a function, $\Pi=\{x_0,\dots,x_n\}$ be a partition and $S=\{c_1,\dots,c_n\}$ a set of values such that $c_i\in[x_{i-1},x_i]$. The Riemann sum is $$R(\Pi,S)=\sum_{i=1}^nf(c_i)(x_i-x_{i-1}).$$
You have a discrete function $f=v$ and you have a partition in first row of the table. Can you find the Riemann sum now?