How do you find the average value of f ( x ) = &#x2212;<!-- − --> x <mrow cl

Thomas Hubbard

Thomas Hubbard

Answered question

2022-05-24

How do you find the average value of f ( x ) = x 5 + 4 x 3 5 x 3 as x varies between [-2, 0]?

Answer & Explanation

Ada Harrington

Ada Harrington

Beginner2022-05-25Added 12 answers

The average value is 1 b a a b f ( x ) d x
We need x n d x = x n + 1 n + 1 + C ( n 1 )
Therefore,
The average value is 1 0 2 2 0 ( x 5 + 4 x 3 5 x 3 ) d x
= 1 2 [ x 6 6 + 4 x 4 4 5 x 2 2 3 x ] 2 0
= 1 2 ( 0 ( 2 6 6 + 16 10 + 6 ) )
= 1 2 ( 32 3 12 )
= 4 6 = 2 3

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