MATH 1552 : Math 1552 Finals Fall 2011
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In order to earn partial credit, please show all of your work: (a) use integration by parts to evaluate the integral (b) evaluate the integral. Sin x dx: (a) use a suitable trigonometric substitution to evaluate the integral (b) evaluate the integral. 1 dx x ln x or show that it is divergent: use partial fraction decomposition to evaluate. Z 5x2 + 3x 2 x3 + 2x2 dx. 4. (a) if the n th partial sum sn of a series p n=1 an is sn = Nd an and p n=1 an. (b) use the integral test to determine whether the series p n=1 or diverges. 1 (4+n)3/2 converges: use either the (basic) comparison test or the limit comparison test to determine if the following series converge or diverge (a) (c) 2: find the radius of convergence and the interval of convergence of the power series.
