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Unformatted text preview: MAC 3473  PRACTICE FINAL EXAM Instructions: Answer all questions. Show all necessary working and reasoning. Write in such a way that any student in the class can follow your work. A Table of Integrals is supplied. Only scientific calculators are allowed. 120 points total. QUESTION 1. (6 + 6 = 12 pts) Let R the region bounded by the curves x = √ y , x = 0, and y = 4. (i) Write down an integral which gives the volume of the solid obtained by rotating R about the xaxis. (ii) Write down an integral which gives the volume of the solid obtained by rotating R about the yaxis. QUESTION 2. (6 + 6 = 12 pts) Evaluate the following integrals. ( a ) Z ln x x 3 dx, ( b ) Z sec 6 xdx. QUESTION 3. (6 + 6 = 12 pts) Evaluate the following definite integrals. Improper integrals should be evaluated using limits. ( a ) Z 2 2 / √ 3 dx x 2 √ x 2 1 , ( b ) Z ∞ xe 3 x dx. QUESTION 4. (2 + (3 + 3) + 4 = 12 pts) (i) Define what it means for the number L to be a limit of the sequence { a n } ∞ n =1...
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This note was uploaded on 06/03/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.
 Spring '08
 Bonner
 Integrals

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