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Lecture

6.5 Average Value of a Function Question #1 (Easy)


Department
Mathematics
Course Code
MAT136H1
Professor
all

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6.5 Integral Applications
Average Value of a Function
Question #1 (Easy): Finding the Average Value of a Polynomial Function
Strategy
Average value of a function is determined by adding all the data points , then dividing it by the
number of data points . Rearranging   
gives  
 .
Thus, 




 .
As   : 
 

 . Therefore, 

.
Sample Question
1) Find the average value of the function over the interval .
2) Find the value of so that  .
Solution
1) Average value of a function:

Given the interval  ,   and  . Substitute into the equation:








Therefore, the average value of the function  over the interval  is .
2) Since  
, and  , then set these equal to each other:
 
, then 

; 
; 
. So finally 
.
Therefore,  
where .