Chapter 14.1, Problem 23ES

Determine whether the statement is true or false. Explain your answer.

In the definition of a double integral

${\displaystyle \underset{R}{\iint }f\left(x,y\right)dA=\underset{n\to +\infty }{\lim }}{\displaystyle \underset{k=1}{\overset{n}{\sum }}f\left(x_k^{*},y_k^{*}\right)\nabla A_k}$

the symbol $\Delta A_k$ represents a rectangular region within $R$ from which the point $\left(x_k^{*},y_k^{*}\right)$ is taken.