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I'm really trying - Integral Help Please

  • Thread starter 1MileCrash
  • Start date
  • #1
1,331
45

Homework Statement


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




Homework Equations





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?
 

Answers and Replies

  • #2
1,331
45
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).
 
  • #3
2,571
1
Do the indefinite integral first
 
  • #4
1,331
45
Worked it again and got it right. Need some practice.
 

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