What is the average value of the function f ( x ) = ( x &#x2212;<!-- − --> 1

Devin Anderson

Devin Anderson

Answered question

2022-06-24

What is the average value of the function f ( x ) = ( x 1 ) 2 on the interval from x=1 to x=5?

Answer & Explanation

g2joey15

g2joey15

Beginner2022-06-25Added 21 answers

Explanation:
The average value of a function f on an interval [a,b] is
1 b a a b f ( x ) d x
So the value we seek is
1 5 1 1 5 ( x 1 ) 2 d x = 1 4 [ ( x 1 ) 3 3 ] 1 5
= 1 12 [ ( 4 ) 3 ( 0 ) 3 ]
= 16 3

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