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Integration word problem

  1. Sep 29, 2008 #1
    1. The problem statement, all variables and given/known data
    In a West Texas school district the school
    year began on August 1 and lasted until May
    31. On August 1 a Soft Drink company in-
    stalled soda machines in the school cafeteria.
    It found that after t months the machines
    generated income at a rate of
    f(t) =
    500t/ (5t^2 + 2)
    dollars per month. Find the total income,
    $Tsec, produced during the second semester
    beginning on January 1.

    2. Relevant equations

    I know to find the income we first have to find the integral for the function t. I did this and got 50 ln [5x^2 +2].
    I set u = 5t^2 +2, so du = 10t dt

    3. The attempt at a solution

    I used 6 as my upper limit and 1 as my lower limit but I can't get the right answer. Can someone please tell me what is the right limit of integration to use in this case?
    Thank you so much for your help!
  2. jcsd
  3. Sep 29, 2008 #2


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    Homework Helper

    Your limits are a little off. Why did you use 6? The machine was functioning for 5 months from Aug 1 to Jan 1 the next year. And it's not supposed to be 0 either for the lower limits. That ignores the revenue for the first month.
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