How do you find the average value of the function for f ( x ) = <msqrt> 2 x

Jaqueline Kirby

Jaqueline Kirby

Answered question

2022-06-13

How do you find the average value of the function for f ( x ) = 2 x 1 , 1 x 5?

Answer & Explanation

Govorei9b

Govorei9b

Beginner2022-06-14Added 21 answers

We need
x n d x = x n + 1 n + 1 + C ( n 1 )
The average value is
y ¯ = 1 5 1 1 5 ( 1 2 x 1 ) d x
Perform first the integral by substitution
Let u = 2 x 1 , , d u = 2 d x
Therefore,
( 1 2 x 1 ) d x = 1 2 d u u = 1 2 2 u = u = 2 x 1
So
y ¯ = 1 4 [ 2 x 1 ] 1 5 = 1 4 ( ( 9 ) ( 1 ) ) = 1 4 2 = 1 2

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