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\leftline{Mathematics 134 -- Intensive Calculus for Science 2}
\leftline{Exam I -- February 17, 2006}
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{\it Directions}.  Do all work in the blue exam booklet.  You
may use a calculator on any of the following problems.  There are
100 possible points.
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I.  The given graph shows $y = f(x)$. 
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\item{A)} (10)  Use the graph to determine $\int_0^4 f(x)\ dx$.
\item{B)}  (5) Let $F(x)$ be the antiderivative of $f(x)$
with $F(0) = -2$.  What is $F(4)$?
\item{C)}  (15) Give a qualitative sketch of $y = F(x)$
from part B.  Your graph should show where $F$ is 
increasing/decreasing, and where $F$ is concave up/concave down.
\item{D)} (5) The function $G(x)$ is $G(x) = \int_0^x f(t)\ dt$
using the function $f$ in the graph above.  What is $G'(2)$?
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II.  On the Moon, the acceleration due to gravity is about -1.6 m/sec${}^2$
(versus about -9.8 m/sec${}^2$ on Earth).  
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\item{A)} (10) A rock is tossed upward with initial velocity $v(0) = 1$
 m/sec.  
Solve the equation ${dv\over dt} = -1.6$ to find 
the velocity of the ball as a function of time. 
\item{B)} (10) Use your answer $v(t)$ from part A.  If the 
rock's initial height is $h(0) = 1$ m,  solve the equation 
${dh\over dt} = v(t)$ to find the height of the rock as a function 
of time.   
\item{C)}  (10) How long does the rock take to fall back 
to ground level on the Moon?  Would the corresponding time be longer
or shorter on the Earth?
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III.  Compute each of the integrals below using basic rules
and/or substitution.  You must show all work
for full credit. 
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\item{A)} (10) 
$$\int 3x^7 - {4\over x^3} + 5\sqrt{x} + {7\over x}\ dx$$
\item{B)} (15)
$$\int_0^1 \sin(\pi x) + \cos(\pi x)\ dx$$
\item{C)} (10) 
$$\int x e^{5x^2 + 7}\ dx$$
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