Math 126 Fall 2003

Math 126 Fall 2003 - MATH 126 FINAL EXAM Read the problems...

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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 y -axis 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 0 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 density ρ find the work done in pumping the liquid over the top rim of the cone.
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