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Calculus  II                                                          Test #1                                                  March 3, 2004

Name____________________                     R.  Hammack                                                Score ______
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(1) Find the following antiderivatives.

(a)

(b)

(c)

(d)

(e)

(f)

(2) Use Part 2 of the Fundamental Theorem of Calculus to write an antiderivative of

(3) Find the following definite integrals. (You may use any technique. Sometimes area may be the best approach.)

(a)

(b)

(c)

(d)

(e)
(Because graph of integtrand is half a circle of radius 2)

(f)

(4)  Use the definition of the definite integral to write    as a limit of Riemann sums.
(You do not need to find the value of this integral -- just write down the limit,)

By setting , and , this becomes

(5)  Find the average value of on the interval [0, 4].

(6) Find the derivatives of the following functions.

(a)

(b)

(7) Suppose a particle moves along the s-axis in such a way that its acceleration at time t seconds is units per second per second. Suppose that   and  .  Find the position function .

Now, , which becomes , so the velocity function is .

Next, .
Now, , which becomes , and C=7.

Therefore, the position function is .

(8) Suppose that     and  .

(a)

(a)

Note that
Thus,
Plugging in the known information, we get
, so