How do you find the average value of f ( x ) = x <mrow class="MJX-TeXAtom-ORD"

Jude Hunt

Jude Hunt

Answered question

2022-05-20

How do you find the average value of f ( x ) = x 5 4 x 3 + 2 x 1 as x varies between [-2,2]?

Answer & Explanation

Melina Glover

Melina Glover

Beginner2022-05-21Added 11 answers

The average value of a function is found using the following equation:
f a v e = 1 b a a b f ( x ) d x
on some interval [a,b]
Therefore:
f a v e = 1 4 2 2 ( x 5 4 x 3 + 2 x 1 ) d x
This is a basic integral.
f a v e = 1 4 ( 1 6 x 6 x 4 + x 2 x ) ] 2 2
= 1 4 4
=-1

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