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Lecture

# 6.5 Average Value of a Function Question #2 (Medium)

Department
Mathematics
Course Code
MAT136H1
Professor
all

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6.5 Integral Applications
Average Value of a Function
Question #2 (Medium): Finding the Average Value of a Trigonometric Exponential Function
Strategy


Make sure to integrate correctly, then divide by    to get the average value of the function.
Sample Question
Find the average value of the function over the interval .

Solution
Average value of a function:

Given the interval  ,   and   .
Notice the function  is in the form of chain rule.
So,  
 (to check, take the derivative and see if it equals to 
Substituting into the equation: 





  


 

 
  
Therefore, the average value of the function
 over the interval  is
 
 
.