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e204k - Exam II MAC 2312 S Hudson Show all your work Use...

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Exam II July 27, 2004 MAC 2312 S Hudson Show all your work. Use the space provided, or leave a note. Don’t use a calculator or your own extra paper. Use these formulas as needed: sin n x dx = - 1 n sin n - 1 x cos x + n - 1 n sin n - 2 x dx u a + bu du = 2 15 b 2 (3 bu - 2 a )( a + bu ) 3 / 2 + C u du a + bu = 2 3 b 2 ( bu - 2 a ) a + bu + C 1) (10pt) Find the arc length of the curve y = 3 x 3 / 2 - 1 from x = 0 to x = 1. 2) (10pt) A cylindrical tank is 9 ft tall, has a radius of 5 ft, and is 2/3 full of water (62 lbs per cu.ft.). Use an integral to find the work required to pump the water out the top of the tank. [Compute the integral, but you do not have to multiply out the constants]. 3) (40pts) Compute each one: a) xe - x dx b) sin 4 ( x ) dx = c) 3 2 x dx = d) x 2 x - 3 dx e) 1 - 1 1 1+ x 2 dx 1
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4) (15pts) a) Write down the definition of ln(1 . 6) (it is a definite integral). 4b) Write down the formula for Simpson’s Rule. 4c) Use Simpson’s Rule with n = 6, and the integral in 4a), to approximate ln(1 . 6). The following table may help (but not all the numbers are useful).
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