How do you find the average value of the function for f ( x ) = <msqrt> x </msqrt

civilnogwu 2022-07-07 Answered
How do you find the average value of the function for f ( x ) = x + 1 x , 1 x 9?
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Answers (1)

Zackery Harvey
Answered 2022-07-08 Author has 21 answers
Use the formula 1 b a a b f ( x ) d x and the Fundamental Theorem of Calculus (FTC) to get an average value equal to 8 3 .
Explanation:
The average value is 1 b a a b f ( x ) d x = 1 9 1 1 9 ( x 1 2 + x 1 2 ) d x.
The FTC then leads us to say this equals
1 8 ( 2 3 x 3 2 + 2 x 1 2 ) | 1 9 = 1 8 ( ( 2 3 27 + 2 3 ) ( 2 3 1 + 2 1 ) )
This simplifies to
1 8 ( 24 8 3 ) = 1 8 ( 64 3 ) = 8 3
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