Chapter 14.1, Problem 26ES

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

Suppose that for some region $R$ in the $xy\text{-plane}$ ${\displaystyle \underset{R}{\iint }f\left(x,y\right)dA}=0$

If $R$ is subdivided into two regions $R_1$ and $R_2,$ then ${\displaystyle \underset{R_1}{\iint }f\left(x,y\right)dA=-{\displaystyle \underset{R_2}{\iint }f\left(x,y\right)dA}}$