How do you find the average value of the function for f ( x ) = x sin &#x2061;<!--

Matilda Webb

Matilda Webb

Answered question

2022-05-12

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

Answer & Explanation

Sage Guerra

Sage Guerra

Beginner2022-05-13Added 10 answers

Explanation:
The average value of a function continuous on [a,b] is given by
A = 1 b a a b f ( x ) d x
Thus
A = 1 2 π 0 0 2 π x + sin x
A = 1 2 π [ 1 2 x 2 cos x ] 0 2 π
A = 1 2 π ( 1 2 ( 4 π 2 ) 1 + cos ( 0 ) )
A = 1 4 π ( 4 π 2 )
A = π
Hence, the average value of the given function on the interval 0 x 2 π i s π .

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