Chapter 15.5, Problem 12ES

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

If $\sigma$ is the portion of a plane of a plane $z=c$ over a region R in the $xy\text{-plane,}$ then

${\displaystyle \underset{\sigma }{\iint }f\left(x,y,z\right)dS}={\displaystyle \underset{R}{\iint }f\left(x,y,c\right)dA}$

for every continuous function $f\text{on}\sigma \text{.}$