Pre-Video Questions

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Before watching the videos, think about and answer these questions to the best of your ability.

Ana left home to go on a bike ride. Let $v(t)$ represent Ana’s velocity (in miles per hour) $t$ hours after she left home. Which of the following best describes the meaning of $\int _{0.5}^{2} v(t) dt$ ?

The change in Ana’s velocity from 0.5 hours to 2 hours after she left home. The change in Ana’s distance away from home from 0.5 hours to 2 hours after she left home. Ana’s average speed from 0.5 hours to 2 hours after she left home. Ana’s distance away from home 1.5 hours after she left home.

If $m$ and $n$ are constants, which of the following expressions is equal to $\int _n^m \cos (x) dx$ ?

$-\sin (m) + \sin (n)$ $\cos (m) - \cos (n)$ $\sin (m) - \sin (n)$ $\cos (n) - \cos (m)$ $\sin (n) - \sin (m)$