# I'm really trying - Integral Help Please

## 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

$C = 15te^{-0.2t}$

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

## The Attempt at a Solution

I want to find the definite integral of

$C = 15te^{-0.2t}$

From t = 0 to t = 3.

$\int^{3}_{0}15te^{-0.2t}dt$

$u = 15t$
$du = 15 dt$
$v = \frac{-e^{-0.2t}}{0.2}$
$dv = e^{-0.2t}dt$

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

$\frac{-15te^{-0.2t}}{0.2}^{3}_{0}$ - $\int^{3}_{0} \frac{-15e^{-0.2t}}{0.2}dt$

$123.4862 - 13.720 + 25$

Which I know is wrong because I just graphed the integral with my calculator. So, where am I being stupid?