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Dye Dilution; Estimate value of an Integral

  1. Jul 10, 2011 #1
    1. The problem statement, all variables and given/known data
    The dye dilution is used to measure cardiac output with 6 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)=20te^(-0.6t), 0 =< t =< 10, where t is measured in seconds. Find the cardiac output.

    2. Relevant equations
    Cardiac output is given by: F=A/[itex]\int[/itex][c(t) dt]010 where the amount of dye A is known and the integral can be approximated from the concentration readings.

    3. The attempt at a solution

    In this case A=6 mg and c(t) = 20te^(-0.6t).

    I've been trying to estimate with a Riemann sum and/or Simpson's rule but I can't figure out how to get the integral in the correct form to estimate with.

    Wolfram alpha spits out 54.5916 using a Riemann sum, but the next problem in this packet (same setup with different dye amount) suggests I use Simpson's rule.

    When I plug values of 0->10 into the function I get weird values but I can't integrate it without an estimation technique.
  2. jcsd
  3. Jul 10, 2011 #2


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    Science Advisor

    That is pretty easy to integrate directly, isn't it? I assume you are required to integrate numerically as practice, but what do you get for the integral, analytically?

    I don't get anything at all like "54..", I get around 30 for the integral and then around 0.2 for the fraction.
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