MATH 1552 : Finals 1552 S13
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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. Z cos2 x sin3 xdx: (a) use a suitable trigonometric substitution to evaluate the integral. Z dx x2 25 x2 (b) evaluate the improper integral. 1 dx x lnx or show that it is divergent: use partial fractions decomposition to evaluate. Z 5x2 + 3x 2 x3 + 2x2 dx: (a) find the exact length of the curve y = ln(cos x), 0 x /3. (b) find the exact area of the surface obtained by rotating the curve x = 1 y 2 about the x-axis. 5. (a) if the nth partial sum of a series p n=1 an is. Nd an and p n=1 an. (b) use the integral test to determine whether the series p n=1 diverges. lnn n3 converges or.
