How do you find the average value of the function for f ( x ) = x <mrow class=

Ainsley Zimmerman

Ainsley Zimmerman

Answered question

2022-05-17

How do you find the average value of the function for f ( x ) = x 2 x , 0 x 3?

Answer & Explanation

Cortez Hughes

Cortez Hughes

Beginner2022-05-18Added 23 answers

Explanation:
Recall the formula for determining the average value of a function f(x) on an interval from [a,b]:
A v g . V a l u e = 1 b a a b f ( x ) d x
For this problem:
A v g = 1 3 0 0 3 ( x 2 x ) d x
= 1 3 0 3 ( x 2 x 1 / 2 ) d x
= 1 3 [ x 3 3 2 3 x 3 2 ] 0 3
= 1 3 ( 3 3 3 2 3 3 3 2 ) = 1 3 ( 27 3 2 3 3 3 )
= 1 3 ( 9 2 3 ) = 3 2 3 3

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