Find the average value of the function on the given interval? f(x)=4x-x^2, [0;4]

Makayla English

Makayla English

Answered question

2023-03-26

Find the average value of the function on the given interval?

Answer & Explanation

anajusthings5mrf

anajusthings5mrf

Beginner2023-03-27Added 10 answers

Average performance of a function = a b f ( x ) d x b - a
Here f ( x ) = 4 x - x 2 and b = 4 , a = 0
So,
f ( x ) a v g = 0 4 ( 4 x - x 2 ) d x 4 - 0
f ( x ) a v g = [ 4 x 2 2 - x 3 3 ] 0 4 4
f ( x ) a v g = [ 4 x 2 2 - x 3 3 ] 0 4 4
f ( x ) a v g = ( 2 × 4 2 - 4 3 3 ) - ( 2 × 0 2 - 0 3 3 ) 4
f ( x ) a v g = 32 3 4
f ( x ) a v g = 8 3
f ( x ) a v g = 2.66

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