Chapter 14.1, Problem 24ES

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

If $R$ is the rectangle $\left\{\left(x,y\right):1\le x\le 4,0\le y\le 3\right\}\text{and}{\displaystyle {\int }_0^{3}f\left(x,y\right)dy=2x,\text{then}}$ ${\displaystyle \underset{R}{\iint }f\left(x,y\right)dA=15}$