Answer:
2080
Step-by-step explanation:
Given: [tex]r(t)=400+800t-120t^2[/tex]
Looking for: [tex]\int\limits^{t_2}_{t_1} {r} \, dt[/tex]
Solve:
[tex]\int\limits^{t_2}_{t_1} {r} \, dt= \int\limits^{2}_{0} ({400+800t-120t^2}) \, dt\\ =(400t+400t^2-40t^3)|^{2}_{0}[/tex]
There is a total of 2080 cars passing through the intersection between 6 am and 8 am and this can be determined by doing integration.
Given :
The traffic flow rate (cars per hour) across an intersection is [tex]\rm r(t)=400+800t-120t^2[/tex], where t is in hours, and (t = 0) is 6 am.
Integration should be carried out to determine the number of cars passing through the intersection between 6 am and 8 am.
[tex]\int\limits^{t_2}_{t_1} {r} \, dt =\int\limits^2_0 {400+800t-120t^2} \, dt[/tex]
[tex]=[400t+400t^2-40t^3]^2_0[/tex]
[tex]=400\times 2 +400\times 2^2 - 40\times2^3[/tex]
= 800 + 1600 - 320
= 2080
So, there is a total of 2080 cars pass through the intersection between 6 am and 8 am.
For more information, refer to the link given below:
https://brainly.com/question/22008756
