Calculating Average Temperature Using Integrals

In summary, the conversation discusses finding the average temperature between 9 am and 9 pm in a certain city. The temperature is modeled by the function T(t)=50 + 14 sin (Pi t / 12) and the individual is attempting to use integration to find the answer. After some confusion with the limits, it is determined that the correct limits to use are a = 9 and b = 21 (using 24-hour notation).
  • #1
badtwistoffate
81
0
A certain city, the temp in degrees Farenheit, t hrs after 9 am was modeled by the function: T(t)=50 + 14 sin (Pi t / 12)
Find avg temp during the period from 9 am to 9 pm.

What i did was take the Int[50 + 14 sin (Pi t / 12),t,0,9]... but this doesn't produce the answer. It says model after 9 am so at 9=0 for a , b = 10 for 9pm?
Any help?
 
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  • #2
shouldnt b be 12 and not 10 since it is 12 hours from 9am - 9pm
 
  • #3
Set your limits a,b to a = 9 and b = 21 (using 24-hr notation)
 
  • #4
i tried 9 to 21 and it didnt work before...
 
  • #5
it works from 0 to 12, thanks, don't know why i thought 10 DUH
 

Related to Calculating Average Temperature Using Integrals

1. What is the "Integral Average Question"?

The Integral Average Question is a mathematical concept that asks for the average value of a function over an interval. It is used in calculus to find the average rate of change of a function over a given interval.

2. How is the Integral Average Question different from the Average Value Theorem?

The Integral Average Question and the Average Value Theorem are related concepts, but they are not the same. The Integral Average Question gives the average value of a function over an interval, while the Average Value Theorem states that there is a point in the interval where the function takes on its average value.

3. How is the Integral Average Question used in real life?

The Integral Average Question has many real-life applications, such as calculating the average speed of a moving object, finding the average temperature over a period of time, and determining the average cost of a product or service.

4. What is the formula for solving the Integral Average Question?

The formula for solving the Integral Average Question is:
Average value = (1/b-a) ∫ba f(x)dx
Where a and b are the lower and upper limits of the interval, and f(x) is the function being integrated.

5. Can the Integral Average Question be applied to any type of function?

Yes, the Integral Average Question can be applied to any continuous function over a closed interval. However, if the function is not continuous, the average value may not exist.

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