Chapter 5.4, Problem 26ES

For a function $f$ that is continuous on $\left[a,b\right]$ , Definition $\mathrm{5.4.5}$ says that the net signed area $A$ between $y=f\left(x\right)$ and the interval $\left[a,b\right]$ is

$A=\underset{n\to +\infty }{\lim }{\displaystyle \underset{k=1}{\overset{n}{\sum }}f\left(x_k^{*}\right)}\Delta x$

Give geometric interpretations for the symbols $n,x_k^{*}$ , and $\Delta x$ . Explain how to interpret the limit in this definition.