The number of chips tested between 11:00 a.m. and 3:00 p.m. is the difference between the number of chips tested at t = 6 and t = 2. So, the number of chips tested between 11:00 a.m. and 3:00 p.m. is 68.
Given the rate of chips per hour,
3t^2 + 16t +5 , where (0 ≤ t ≤ 6)
We have to calculate the chip tested between 11:00 a.m to 3:00p.m.
Assume t = 0 for 9:00 a.m (given in the question)
So from above we came put the value of t = 2 ,for 11:00 a.m and t = 6 for 3:00 p.m .
Now integrating the equation ,
[tex]\int\limits^6_2 {(-3t^2 + 16t + 5)} \, dt[/tex]
Integrating an equation involves finding a function that represents the area under the curve defined by the equation. This process is also known as finding the indefinite integral of the equation.
By solving ,
-t^3 + 8t^2 +5, where t varies from t = 2 to t = 6;
substituting the value of t, we get the value of integration as 68
∴ 68 is the answer.
Complete question :
A technician can test video player chips at the rate of -3t^2 + 16t + 5 chips per hour (for 0 ≤ t ≤ 6), where t is the number of hours after 9:00 am. How many chips can be tested between 11:00 a.m. to 3:00 p.m.?
To learn more about integrating refer :
https://brainly.com/question/24168257
#SPJ1
