# Dye Dilution; Estimate value of an Integral

1. Jul 10, 2011

### oddjobmj

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/$\int$[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. Jul 10, 2011

### HallsofIvy

Staff Emeritus
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.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook