Answer
$4048~$ calculators are produced from the beginning of the third week to the end of the fourth week.
Work Step by Step
Note that we can think of the beginning of the third week as the end of the second week.
We can find the number of calculators produced from the beginning of the third week to the end of the fourth week:
$\int_{2}^{4}5000~\left(1-\frac{100}{(t+10)^2}\right)~dt$
Let $u = t+10$
$\frac{du}{dt} = 1$
$dt = du$
When $t = 2$, then $u = 12$
When $t= 4$, then $u = 14$
$\int_{12}^{14}5000~\left(1-\frac{100}{u^2}\right)~du$
$=5000\left(u+\frac{100}{u}\right) ~\Big\vert_{12}^{14}$
$=5000~[(14+\frac{100}{14})-(12+\frac{100}{12})]$
$=5000~(\frac{296}{14}-\frac{244}{12})$
$\approx 4048$
$4048~$ calculators are produced from the beginning of the third week to the end of the fourth week.
