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

Crystal Wheeler 2022-07-04 Answered
How do you find the average value of f ( x ) = x 5 + 3 x 3 as x varies between [0,1]?
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Answers (1)

Dayana Zuniga
Answered 2022-07-05 Author has 16 answers
The average value of the function f on [a,b] is found through
1 b a a b f ( x ) d x
Which here gives us the average value
1 1 0 0 1 ( x 5 + 3 x 3 ) d x
Integrating term by term using x n d x = x n + 1 n + 1 gives
= [ x 6 6 + 3 x 4 4 ] 0 1
The 0 part of this will still be 0, leaving us with just
1 6 + 3 4 = 7 12

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