Question

The traffic flow rate (cars per hour) across an intersection is r ( t ) = 400 + 800 t − 120 t 2 , where t is in hours, and t =0 is 6am. How many cars pass through the intersection between 6 am and 8 am?

Answer 1

Answer:

2080

Step-by-step explanation:

Given: $r(t)=400+800t-120t^2$

Looking for: $\int\limits^{t_2}_{t_1} {r} \, dt$

Solve:

$\int\limits^{t_2}_{t_1} {r} \, dt= \int\limits^{2}_{0} ({400+800t-120t^2}) \, dt\\ =(400t+400t^2-40t^3)|^{2}_{0}$