e107k

# e107k - Exam I and Key MAC 2312 S Hudson 1(15 pts Answer...

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Exam I and Key July 12, 2007 MAC 2312 S Hudson 1) (15 pts) Answer True or False in the margin. You don’t have to explain. There is a point c in [0, π ] such that sin( c ) = R π 0 sin( x ) dx . If f is not bounded on [a,b] then it is not integrable on [a,b]. Displacement is always less than or equal to distance travelled. For the shell method about the y -axis, the formula is V = R b a 2 πxf ( x ) dx . A cube is an example of a right cylinder. 2)(15pts) Find the area under y = x 2 over the interval [0,1] using a limit of right end- point approximations. Draw a picture, show your work, and [hint!] use formulas like Σ( k/n ) 2 (1 /n ) and/or n ( n + 1)(2 n + 1) / 6 along the way. 3) (10 points each) Calculate, and show work. Explain any non-obvious steps brieﬂy. a) R π/ 4 0 sin 2 x dx = b) R 3 0 | x - 2 | dx = c) R 2 1 dx 5 x - 1 = d) Find the area between y = x 2 and x = y - 2. 4)(15 pts) A ball is thrown upwards from ground level with an initial velocity of 16 ft/sec. Find a formula for its height using antiderivative(s). [Recall that

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## This note was uploaded on 12/26/2011 for the course MAC 2312 taught by Professor Storfer during the Summer '08 term at FIU.

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e107k - Exam I and Key MAC 2312 S Hudson 1(15 pts Answer...

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