e211k - Exam II and Key MAC 2312 July 19, 2011 S Hudson 1-3...

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Exam II and Key July 19, 2011 MAC 2312 S Hudson 1-3 (10 points each) Set up each of these problems, by writing down the definite integrals that solve them. Show some work, such as a sketch, background formulas, and/or a brief discussion. But you do not have to evaluate them. 1) Find the arc length of the parametric curve x = t 3 / 3, y = t 2 / 2, with 0 t 1. 2) Find the volume of the solid that results when the region enclosed by y = x , y = 0 and x = 9 is revolved about the line x = 9. State at the start whether you are using disks, washers or shells. Set-up only. 3) A spring exerts a force of 6 N when stretched from its natural length of 4 m to a length of 4.5 m. Find the work required to stretch the spring 2 m beyond its natural length. [I do not care much about the units - you can replace N by lbs and m by ft]. Set-up only. 4) [10pts] Compute the average value of f ( x ) = sin(2 x ) on [ π/ 2 ]. 5) [10pts] Compute
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e211k - Exam II and Key MAC 2312 July 19, 2011 S Hudson 1-3...

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