ma241exam1-c

# ma241exam1-c - is convergent or divergent. (Again, you must...

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Spring 2007 Therkelsen MA 241 - Exam 1 (C) Instructions Use a blue examination book to answer all parts for each problem below. Be sure to write your name and test form (C) on the front cover of the blue book. Please do not answer more than one problem per page. Leave answers in exact form (for example, 2 instead of 1 . 4142 ... ). Circle or box all Fnal answers (partial credit may be given, but only for work shown). No graphing calculators, cell phones, PDAs, etc. Include this sheet when submitting your exam book. Problems 1. Evaluate 1 Z 0 x 4 x 2 dx 2. Integrate Z x sin 4 xdx 3. Integrate Z x 2 2 x 1 ( x 1)( x 2 +1) dx 4. Determine if the improper integral is convergent or divergent. If it is convergent, evaluate. (You must show your work for full credit.) Z 0 x ( x 2 +4) 2 dx (over) 1

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5. Use the Comparison Theorem for improper integrals to determine if the improper integral
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Unformatted text preview: is convergent or divergent. (Again, you must show your work for full credit.) Z 1 1 sin 2 x x 2 + 1 dx 6. The region enclosed by y = x and y = x 2 is rotated about the x-axis. Sketch the region and Fnd the volume of the resulting solid. 7. Integrate. You may need to use one of the formulas that follow. Z x 2 x 6 16 dx Z p u 2 a 2 du = u 2 p u 2 a 2 a 2 2 ln u + p u 2 a 2 + C Z du u 2 a 2 = ln u + p u 2 a 2 + C Z u 2 du u 2 a 2 = u 2 p u 2 a 2 + a 2 2 ln u + p u 2 a 2 + C Z du u 2 u 2 a 2 = u 2 a 2 a 2 u + C 2...
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## This note was uploaded on 01/25/2011 for the course MA 241 taught by Professor Mccollum during the Spring '08 term at N.C. State.

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ma241exam1-c - is convergent or divergent. (Again, you must...

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