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**Biff** I am not sure how to approach this problem.

**Problem**

Suppose a certain object moves in a straight line with the following velocity, where $\displaystyle v$ is in meters per second and $\displaystyle t$ is in seconds:

$\displaystyle v(t) = -2 + t + 3\sin(\pi t)$

Without using your calculator, but instead using properties of definite integrals and facts you know about area, determine the net change in distance of the object from $\displaystyle t = 0$ to time $\displaystyle t = 6$ and find the object's average velocity on this interval.

My impression is that the net change in distance would be:

$\displaystyle d = \int_{0}^{6} |v(t)| dt$

But since we cannot use our calculators I am unsure.