The sales of a plastic widget were estimated to be:
$P(t) = 8000te ^{−0.5t}$
where $t$ is in weeks, and $P(t)$ is in units per week.
How many widgets were sold in the first $9$ weeks?
To start, I need to definite integral. This means that I need a $v$, $\mathrm{d}v$, $u$, and $\mathrm{d}u$.
I know $u= t$, $du = dt$, $dv = e^{-0.5t}$ and $v= -e^{-0.5t}/{0.5}$
So then it should be
$\int^9_08000te^{-.5t}dt$
After that I should switch it to
$8000\int^9_0te^{-.5t}dt$
But I'm not sure what to do after that point to get the answer.
1 Answer
In order to solve the integral, taking into account you are using parts method:
$uv\int vu' dt$
Solve that indefinite integral (comment if you need help there), compute and then apply the boundaries
And of course, the 8000 must be outside the integral, not duplicated inside.
