Chapter 14.7, Problem 14ES

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

If $\text{r}=x\left(u,\upsilon \right)\text{i}+y\left(u,\upsilon \right)\text{j}$ maps the rectangle $0\le u\le 2,1\le \upsilon \le 5$ to a region R in the xy-plane, then the area of R is given by ${\displaystyle {\int }_1^5{\displaystyle {\int }_0^2\left|\frac{\partial \left(x,y\right)}{\partial \left(u,\upsilon \right)}\right|}}dud\upsilon$