M1272SampleExamProbs1R

# M1272SampleExamProbs1R - Sample Problems for First Mid-term...

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Sample Problems for First Mid-term Exam culled from Spring 2009 exams 1 and 2 (Ruffa) Compute the following integrals: 1) sin 3 3 θ cos 3 d 2) dx x 16 x 2 3) tan 4 x dx 4) t dt t 2 + 4 t 5) a) Find the indefinite integral sin 2 sin 5 d . b) What is the average value of the function f ( ) = sin 2 sin 5 over the interval [ 0 , π /2 ] ? 6) Evaluate the integral cos 1 ( 2 x ) dx 1/ 2 1/ 2 . 7) a) Evaluate the definite integral ( ln x ) 2 x 2 1 e dx . b) Using your work from part (a), show whether (ln x ) 2 x 2 1 dx converges. If it does, what is the value of this improper integral?

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8) a) Determine the indefinite integral 7 x 2 x 12 dx . b) Is 7 x 2 x 12 dx 3 0 convergent? If not, explain why it diverges; otherwise, find its value. 9) a) For the curve y = e x , x 0 , set up the integral to find the surface area produced by revolving the curve about the y -axis. b) Using an argument involving the comparison tests, show that this integral diverges (that is, the surface area produced is infinite). 10) A ball is thrown horizontally from a height H above the ground [ position ( 0, H ) ]
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M1272SampleExamProbs1R - Sample Problems for First Mid-term...

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