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\centerline{Mathematics 132 -- Calculus for Physical and Life Sciences, 2}
\centerline{Discussion 2 -- Practice on Integrals by Substitution}
\centerline{February 2, 2005}
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{\it Goal and Directions}
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We want to practice the substitution method for integration on 
a further collection of examples today.  Each group will first
work out ``their integral'' and put their work up on the board
when they are done.  Then, in additional time, look at the other
integrals and find a likely substitution $u = g(x)$ to 
try.  When all the groups have posted their work, we'll ``compare
notes.''  There will not be an assignment to hand in from today's
work.  But you should take notes on all of the examples as
we go through them.
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{\it Integrals}
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\leftline{Group 1:}  $$\int t e^{t^2}\ dt$$
\leftline{Group 2:}  $$\int x\sqrt{4 - x^2}\ dx$$
\leftline{Group 3:}  $$\int {\cos(\sqrt{y})\over \sqrt{y}}\ dy$$
\leftline{Group 4:}  $$\int \sin(5\theta)\cos^3(5\theta)\ d\theta$$
\leftline{Group 5:}  $$\int {2^t\over 2^t + 1}\ dt$$
\leftline{Group 6:}  $$\int {x\over \sqrt{x + 1}}\ dx$$
\leftline{Group 7:}  $$\int (x + \sin(x))^3(1 + \cos(x))\ dx$$
\leftline{Group 8:}  $$\int {1\over x} \tan(\ln(x))\ dx$$
\leftline{Group 9:}  $$\int {1\over x\ln(x)}\ dx$$
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