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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