How do you find the average value of f ( x ) = 4 &#x2212;<!-- − --> x <mro

spazzter08dyk2n

spazzter08dyk2n

Answered question

2022-05-13

How do you find the average value of f ( x ) = 4 x 2 as x varies between [-2,2]?

Answer & Explanation

pomastitxz27r

pomastitxz27r

Beginner2022-05-14Added 16 answers

since f(x) is continuous on the closed interval [-2,2] then the average value of f(x) from x = -2
to x = 2 is the integral
1 b a a b f ( x ) d x
here [a,b] = [-2,2]
= 1 4 2 2 ( 4 x 2 ) d x
= 1 4 [ 4 x 1 3 x 3 ] 2 2
= 1 4 [ ( 8 8 3 ) ( 8 + 8 3 ) ]
1 4 ( 32 3 ) = 8 3

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