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\leftline{Mathematics 134 -- Intensive Calculus for Science 2}
\leftline{Exam 2 -- March 24, 2006}
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{\it Directions:}  Do all work in the blue exam booklet.  You
may use an approved calculator, and the table of integrals provided,
as directed.  There are 100 possible points.
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I.  Compute each of the integrals below, using some combination
of integration by substitution, parts, and partial fractions.  
{\it You must show all work for full credit.  Applying an entry 
from the integral table is OK if necessary, but that will result 
in a deduction of 3 points per part.}
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\item{A)} (15) $$\int x \cos(4x)\ dx$$
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\item{B)} (15) $$\int {x+3\over x^2 - 6x + 8} \ dx$$
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II.  Compute each of the following integrals using an entry or 
entries from the table of integrals.  Say which entry or entries you 
are using.
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\item{A)} (10) $$\int \sin^4(x)\ dx$$
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\item{B)} (10) $$\int (x^2 + 12) e^{3x}\ dx$$
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III.  (20)  Let $R$ be the region bounded by $y = x^2 + 2$, $y = x$,
$x = 0$ and $x = 1$.   Find the volume of the solid obtained if $R$
is rotated about the line $y = 5$.
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IV.  A long thin straight wire extends from $x = 0$ to $x = 1$ cm.  
The density of the wire at $x$ is $\delta(x) = 2 + \cos(\pi x)$ grams per cm.
\item{A)} (10) Set up, {\it but do not evaluate}
the formula computing the {\it center of mass} of the wire.
\item{B)} (10)  If the midpoint Riemann sum with $n = 10$ is
used to approximate the integral for the total mass, will the result be
an overestimate or an underestimate?  Explain.
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V.  (10)  The graph $y = f(x)$ below shows either a probability density (pdf)
or a cumulative distribution (cdf).  Say which it is, and find the value
of $c$ given in the graph.
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