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Unformatted text preview: MATH 126 FINAL EXAM 12/17/03 Read the problems carefully and answer the questions asked. Write neatly and indicate clearly your answer to each problem. All problems count equally and you are to do all ten problems. You must show your work to obtain full credit. Calculators, note, books, or collaboration with others are not allowed. 1. Let T be the bounded region between the graphs of y = x and y = x 2 . Set up but do not evaluate the integrals representing the volumes for the solids obtained by rotating T about: i) the yaxis ii) the line y = 2. 2. Find (i) Z √ x ln( x ) dx ; (ii) Z (1 sin( x )) 2 cos 2 ( x ) dx. 3. Find Z 1 dx √ 2 x x 2 or explain why it does not exist. 4. Find Z ∞ 1 dx x 2 ( x 2 + 1) or explain why it does not exist. 5. A tank has the shape of a circular cone with its point downward and resting on the ground. The tank is four meters high and the diameter of the circle at the top is three meters. If the tank is filled to the depth of two meters with a liquid of densitymeters....
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This note was uploaded on 09/26/2008 for the course MATH 126 taught by Professor Mikulevicius during the Fall '07 term at USC.
 Fall '07
 Mikulevicius
 Math, Calculus

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