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\centerline{Mathematics 132 -- Calculus for Physical and Life Sciences 2}
\centerline{Discussion 1 -- Practice with Antiderivatives}
\centerline{January 26, 2005}
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{\it Goals}
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Today we want to practice using the antiderivative formulas we introduced
last time, and which are also covered in \S 6.2 of the text.
Work out answers to these problems {\it individually}, then 
compare with your group partners and reconcile any differences.
You will hand in {\it one copy} of your group's work as the 
assignment.
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{\it Discussion Questions}
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A.  Find the following indefinite integrals (antiderivatives).
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\item{1)}  $\int {4\over x^{1/2}} + {3\over x^{1/3}}\ dx$
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\item{2)}  $\int {1 \over \cos^2 x} + {1\over 1 + x^2}\ dx$
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\item{3)}  $\int (x + 1)^3\ dx$
(Hint: multiply out, then integrate) 
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\item{4)}  $\int {t^4 + 3t^2 + 1\over {\root 3\of t}}\ dt$
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\item{5)}  $\int 4\cos(x) - 3\sin(x)\ dx$
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B.  Find the exact values of the following definite integrals
using the Fundamental Theorem.
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\item{1)}  $\int_{0}^1 x^4 + x + 3\ dx$
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\item{2)}  $\int_{e}^{e^2} {4\over x}\ dx$
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\item{3)}  $\int_0^{1/2} {dx\over \sqrt{1 - x^2}}$
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\item{4)}  $\int_{-2}^2 3^x\ dx$
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C.  The {\it average value} of the function $f(x) = 6/x^2$ on the interval
from $x = 1$ to $x = c$ is 1.  Find the value of $c$.
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D.  In A 3, suppose the problem said $\int (x+1)^{33}\ dx$
instead of what is there.  Obviously, you don't want to multiply
out $(x+1)^{33}$(!)  Can you find an indefinite integral
a different way?  (Think Chain Rule, but ``in reverse.'')
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{\it Assignment}
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Group writeups due in class on Monday, January 31.
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