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Unformatted text preview: Exam I July 6, 2011 MAC 2312 and Key S Hudson 1) [30pt] Short calculations, 5 pts each, not much partial credit likely. Simplify terms like sin( ) and e , but not like 121 / 44. a) d dx [ R x te t dt ] b) R 4 x + e x dx c) R 2 1 1 t dt f) R sin 2 x dx e) R 1 dx 2 x f) R 3  x 2  dx = 2) [15pts] State and prove the F.T.C., Part Two, about computing the derivative of a definite integral. You can use other definitions and theorems in your proof  but point out when you are doing so. Partial credit is likely, even with small gaps, if you are making a good effort to explain your reasoning. 3) [15pts] Find the exact area under f ( x ) = x 2 , on [0,2] using a limit of sums (as done in class and in Ch.5.4). Use a regular partition and the Right Endpoint Rule. This is roughly equivalent to asking for the definition of R 2 x 2 dx and a calculation of that. To make this long problem a bit easier, you get an outline and some formulas to choose from (but not all are needed, or even correct). A) The interval [0 , 2] gets split into n parts and x * k is the right endpoint of the k th part. Which two of these formulas are correct (choose and explain) ? x = 1 /n , x = 2 /n , x * k = k/n , x * k = 2 k/n , x * k = 2 k 1 /n . B) Now, we add up the areas of n rectangles to get an estimate of the total area, called E n . Which two of these are correct formulas for E n (choose and explain) ?...
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 Summer '08
 Storfer
 Calculus

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