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\leftline{Mathematics 134 -- Intensive Calculus for Science 2}
\leftline{Quiz 6 -- March 17, 2006}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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Do all work on this sheet (front and back if needed).  You have 15 minutes.
{\it No calculators on this quiz.  If you do the extra credit question,
leave answer in exact form.}  
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A) (10) A thin metal plate has the shape of the region sketched below.
The density of the metal is $\delta(x) = e^{3x}$ $kg/m^2$ at all points. 
Give the integral to compute its {\it total mass} (you do not need 
to compute the value).
\vglue 2.0truein 
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{\it Extra Credit} (5)  Evaluate your integral in part A.  
\vglue 2.0truein
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B) (15) The times students need to complete a final exam
are distributed according to the density function 
$$p(t) = c t^3$$
for $0 \le t \le 3$ hours, and $0$ for all other $t$.  What is the 
value of $c$?  Write down the integral that could be
used to compute the probability that a randomly selected
student takes between 2.5 and 3 hours to complete the exam.
(Again, it's not necessary to compute the integral.)
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