Answer
$~~\int_{1000}^{5000}R'(x)~dx~~$ represents the total increase in revenue when production increases from 1000 units to 5000 units.
Work Step by Step
We can state the Net Change Theorem as follows:
The integral of a rate of change is the net change:
$\int_{a}^{b}F'(x)~dx = F(b)- F(a)$
$R'(x)~~$ is the derivative of the revenue function.
Therefore, $~~\int_{1000}^{5000}R'(x)~dx~~$ represents the total increase in revenue when production increases from 1000 units to 5000 units.
