How do you find the average value of f ( x ) = cos ⁡...

delirija7z

delirija7z

Answered

2022-07-01

How do you find the average value of f ( x ) = cos x as x varies betwen [ 0 , π 2 ]?

Answer & Explanation

Charlee Gentry

Charlee Gentry

Expert

2022-07-02Added 19 answers

The average value of the function f(x) on the interval [a,b] can be evaluated through the following the following expression:
average value = 1 b a a b f ( x ) d x
Here, this gives us an average value of:
1 π 2 0 0 π 2 cos ( x ) d x
Integrating cos ( x ) gives us sin ( x ) :
= 1 π 2 [ sin ( x ) ] 0 π 2
= 2 π [ sin ( π 2 ) sin ( 0 ) ]
= 2 π [ 1 0 ]
= 2 π

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