What is the average value of the function

Kaiden Wilkins

Kaiden Wilkins

Answered question

2022-05-14

What is the average value of the function f ( x ) = x 2 on the interval [0,3]?

Answer & Explanation

Athena Blanchard

Athena Blanchard

Beginner2022-05-15Added 13 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 3 0 0 3 x 2 d x
= 1 3 x 3 3 ] 0 3
= ( 3 ) 3 9 ( 0 ) 3 9 = 3

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