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## 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?