Answer
$212 \ bicycles $
Work Step by Step
Let $r$ be the production rate of bicycles per week. Therefore,
$\dfrac{dr}{dt}=95+3t^2-t$
Integrate the above equation to obtain the number of bicycles produced from the beginning of the second week to the ending of the third week:
$\int_1^{3} dr=\int_1^{3} (95+3t^2-t) \ dt$
or, $ =[95t+t^3-\dfrac{t^2}{2}]_1^{3} $
or, $=[95(3)+(3)^3-\dfrac{(3)^2}{2}]-[95(1)+(1)^3-\dfrac{(1)^2}{2}]$
or, $=212 \ bicycles $
Therefore, the number of bicycles produced from the beginning of the second week to the ending of the third week is: $212 \ bicycles $
