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

Armeninilu

Armeninilu

Answered question

2022-06-10

How do you find the average value of f ( x ) = x 4 2 x 2 + 4 as x varies between [-2,1]?

Answer & Explanation

Jayce Bates

Jayce Bates

Beginner2022-06-11Added 18 answers

Since f(x) is continuous on the closed interval [-2 ,1] the average value is.
1 b a a b f ( x ) d x
where [a,b] is the closed interval.
1 1 + 2 2 1 ( x 4 + 2 x 2 + 4 ) d x
= 1 3 [ ( 1 5 + 2 3 + 4 ) ( 32 5 16 3 8 ) ]
= 1 3 [ 67 15 ( 296 15 ) ] = 1 3 ( 363 15 ) = 121 15

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