e311k - Exam III Aug 2, 2011 MAC 2312 S Hudson Remember...

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Unformatted text preview: Exam III Aug 2, 2011 MAC 2312 S Hudson Remember that some integrals may be improper, and that some could benefit from a u substitution (or some algebra) before applying fancier methods. When in doubt, u = e x or u = x 2 is often a good try. 1) (10pts each) Compute the integrals: a) R x 3 e x 2 dx b) R tan 5 sec d c) R e 3 x dx e 2 x +1 2) (5pts each) Compute the integral (or show that it diverges): a) R +1- 1 dx x 2 = b) R + e- x dx x = 3) (10 pts) Start on this by showing the partial fraction splitting, with A , B etc. But you dont have to compute these constants or get an antiderivative; R 2 x- 3 x 3- x 2 = 4) [10 pts] Approximate R +1- 1 e- x 2 dx by S 4 (Simpsons Rule with n = 4). You can use any of the following data from my calculator that you need. Dont leave any variables in your answer, but a few plus signs and fractions are OK. e 1 = 2 . 7 e 1 / 2 = 1 . 6 e 1 / 4 = 1 . 3 e 1 / 16 = 1 . 06 e- 1 = 0 . 37 e- 1 / 2 = 0 . 61 e- 1 / 4 = 0 . 78 e- 1 / 16...
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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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e311k - Exam III Aug 2, 2011 MAC 2312 S Hudson Remember...

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