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e207k

# e207k - Exam II and Key MAC 2312 S Hudson 1[10 pts each...

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Exam II and Key July 25, 2007 MAC 2312 S Hudson 1) [10 pts each] Just set-up each problem below. For each, write the answer as an integral (such as 2 1 x 2 dx ). You don’t have to compute the integrals. 1a) Find the arc length of the curve defined parametricly by x = (1 + t ) 2 , y = (1 + t ) 3 for 0 t 1. 1b) Suppose a 100 ft chain hangs from the top of a tall building. It weighs 12 lbs per foot. How much work is required to pull the chain to the top? 1c) Find the volume, when the region enclosed by x = y and x = y/ 4 is revolved around the x -axis. 2) [10 points each] Calculate, and show work. Explain any non-obvious steps briefly. 2a) tan - 1 (3 x ) dx = 2b) e x sin x dx = 2c) tan 2 x sec 2 x dx = 2d) dx x 2 9 - x 2 = 2e) dx x 2 - 4 x +5 = 3)(10 pts) Start on these two partial fractions problems. You can stop when you have included all the constants A , B , C etc, that you’d need (you don’t have to compute them, and don’t have to compute any anti-derivatives).

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