Pre-Video Questions

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

Determine an antiderivative for $f(x)=\sin (x^2)$

$2x \cos (x^2)$ $-\cos \left ( \frac {x^3}{3} \right )$ $\int _0^x \sin (t^2) dt$ $\int _0^x 2t \cos (t^2) dt$ $\int _0^x -\cos \left ( \frac {t^3}{3} \right ) dt$ $f(x)$ doesn’t have an antiderivative

If $F(x) = \int _0^x e^{2t} dt$ , what is $F’(x)$ ?

$2e^{2x}$ $e^{2x}$ $\dfrac {e^{2x}}{2}$ $\dfrac {e^{2x+1}}{2x+1}$ $\dfrac {e^{2x}}{2}-\dfrac {1}{2}$ $\dfrac {e^{2x+1}}{2x+1}-e$ $\int _0^x 2e^{2t} dt$

$F(x) = \int _0^x 3t-9 dt$ . On the interval $[0,3]$ , $F(x)$ is:

Increasing Decreasing Constant Both increasing and decreasing Can’t tell without more information

The following graph is of $y = f(t)$ over the interval $[-1,4]$ .

Which of the following choices could be the corresponding graph of $F(x) = \int _{-1}^x f(t) dt$ :

Graph a	Graph b	Graph c	Graph d
Graph e	Graph f	Graph g	Graph h