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I'm really trying - Integral Help Please

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data
    The concentration, C, in ng/ml of a drug in the blood as a function of time in hours since the drug was administered is given by

    [itex]C = 15te^{-0.2t}[/itex]

    The area under the curve is the bioavailability, find it from t = 0 to t = 3




    2. Relevant equations



    3. The attempt at a solution

    I want to find the definite integral of

    [itex]C = 15te^{-0.2t}[/itex]

    From t = 0 to t = 3.

    [itex]\int^{3}_{0}15te^{-0.2t}dt[/itex]

    [itex]u = 15t[/itex]
    [itex]du = 15 dt[/itex]
    [itex]v = \frac{-e^{-0.2t}}{0.2}[/itex]
    [itex]dv = e^{-0.2t}dt[/itex]

    Now, I see this as a perfectly good setup for integration by parts. Now, to set up definite integral formula.

    [itex]\frac{-15te^{-0.2t}}{0.2}^{3}_{0}[/itex] - [itex]\int^{3}_{0} \frac{-15e^{-0.2t}}{0.2}dt[/itex]

    [itex]123.4862 - 13.720 + 25[/itex]

    Which I know is wrong because I just graphed the integral with my calculator. So, where am I being stupid?
     
  2. jcsd
  3. Sep 13, 2011 #2
    I was taught that I could evaluate definite integrals by solving uv for the upper limit, then subtracting uv evaluated at lower limit (as if it were an integral using 1st fundamental theorem), and then subtract the integral of vdu (also using fundamental theorem).
     
  4. Sep 13, 2011 #3
    Do the indefinite integral first
     
  5. Sep 13, 2011 #4
    Worked it again and got it right. Need some practice.
     
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