Answer
$~~\int_{0}^{8}r(t)~dt~~$ represents the number of barrels of oil that are consumed from January 1, 2000 until December 31, 2007.
Work Step by Step
We can state the Net Change Theorem as follows:
The integral of a rate of change is the net change:
$\int_{a}^{b}F'(x)~dx = F(b)- F(a)$
$~~r(t)~~$ is the rate at which the world's oil is consumed.
Therefore, $~~\int_{0}^{8}r(t)~dt~~$ represents the number of barrels of oil that are consumed from January 1, 2000 until December 31, 2007.
