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\centerline{Mathematics 134 -- Intensive Calculus for Science 2}
\centerline{Discussion 3 -- Some interesting integrals!}
\centerline{Wednesday January 31, 2001}
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{\it Background}
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Today, we want to practice using the substitution method 
to evaluate some indefinite integrals.  Instead of 
writing up a set of solutions to be handed in, each group will
put their work on the blackboard, and we will discuss the answers
as a group. 
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{\it Group 7}
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\item{A)}  Use the substitution $u = x^2 + 1$ to evaluate
$$\int 4x(x^2+1)\ dx$$
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\item{B)}  Evaluate 
$$\int (\cos(4x) + 7)^3\sin(4x)\ dx$$
by an appropriate substitution.
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\item{C)}  There is a trig identity that says
$$\sin(x)\cos(x) = {1\over 2}\sin(2x)$$
Use this, and an appropriate substitution to evaluate
$$\int\sin(x)\cos(x)\ dx$$
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