How do you find the average value of

Ryker Stein

Ryker Stein

Answered question

2022-05-24

How do you find the average value of f ( x ) = cos x as x varies between [1,5]?

Answer & Explanation

Alberto Duffy

Alberto Duffy

Beginner2022-05-25Added 5 answers

The average value of the function f on the interval [a,b] is
1 b a a b f ( x ) d x
With the given information this translates into
1 5 1 1 5 cos ( x ) d x
The antiderivative of cos ( x ) is sin ( x ) so
= 1 4 [ sin ( x ) ] 1 5 = 1 4 ( sin ( 5 ) sin ( 1 ) )
This is as simplified as we can get without using a calculator.
1 4 ( sin ( 5 ) sin ( 1 ) ) 0.45010

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