Calculus (3rd Edition)

$212 \ bicycles$
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: $212 \ bicycles$