How do you find the average value of

landdenaw

landdenaw

Answered question

2022-06-22

How do you find the average value of sin x as x varies between [ 0 , π ]?

Answer & Explanation

Jaida Sanders

Jaida Sanders

Beginner2022-06-23Added 18 answers

Explanation:
The average value of a function f on the interval [a,b] is found through the integral expression
1 b a 1 b f ( x ) d x
Here, this gives us an average value of
1 π 0 0 π sin ( x ) d x
The antiderivative of sin ( x ) is cos ( x ) :
= 1 π [ cos ( x ) ] 0 π
= 1 π ( cos ( π ) ( cos ( 0 ) ) )
= 1 π ( ( 1 ) ( 1 ) )
= 2 π

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