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Unformatted text preview: MAC 2312 TAKE-HOME QUIZ 2 Spring 2010 NAME UFID: Please show all your work. The answers without the solution will NOT be graded. This take-home quiz is to be taken by yourself. You ARE allowed to use your textbook, class notes, and your calculator. However, you are NOT permitted to talk to anyone (living or dead) about these questions other than Mr. Harrington. You are also NOT permitted to use any other material that is not listed above, like the internet, or a different textbook. You will need to turn in this sheet with your work. 1. Using trigonometric substitution derive ONE (and only ONE) of the following formulas. Assume a > 0. (a) a2 - u2 du = u a2 - u2 + a +C u u2 - a2 | + C a2 - u2 - a ln (b) u2 - a2 u2 - a2 du = - + ln |u + u2 u 2. A gasoline storage tank in the shape of a right cylinder of radius 3 f t and length 12 f t is buried in the ground in the horizontal position. If the top of the tank is 4ft below the surface, find the work required to empty a full tank of gasoline weighing 42 lb/f t3 by pumping it though a pipe that extends to a height of 2 ft above the ground. For full credit, you only need to justify the integral for work. For EXTRA credit, evaluate that integral. 3. Exploring integration by parts. (a) Suppose that f (a) = f (b) = 0 and that the second derivative is continuous on [a, b]. Show that
b b a (x - a)(x - b)f (x)dx = 2 0 f (x)dx
a (b) Using part (a), evaluate x(x - ) sin(x)dx. By signing above you are agreeing with this statement: On my honor, I have neither given nor received unauthorized aid in doing this quiz. ...
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This note was uploaded on 07/11/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.
- Spring '08