How do you find the average value of the function for f ( x ) = 2 &#x2212;<!-- − -->

Yahir Crane

Yahir Crane

Answered question

2022-06-14

How do you find the average value of the function for f ( x ) = 2 1 2 x , 0 x 4?

Answer & Explanation

Donavan Scott

Donavan Scott

Beginner2022-06-15Added 22 answers

Average value of a function is given by
A = 1 b a a b f ( x ) d x
A = 1 4 0 4 2 1 2 x d x
A = 1 4 [ 2 x 1 4 x 2 ] 0 4
A = 1 4 ( 2 ( 4 ) 1 4 ( 4 ) 2 )
A = 1 4 ( 8 4 )
A = 1 4 ( 4 )
A=1
Amber Quinn

Amber Quinn

Beginner2022-06-16Added 3 answers

Explanation:
The average value of a function over an interval is its (definite) integral over that interval divided by the length of the interval.
0 4 ( 2 x 2 ) d x = [ 2 x x 2 4 ] 0 4
=4-0
=4
0 4 ( 2 x 2 ) d x 4 0 = 4 4 = 1
The average value of f over [0,4] is 1.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?