How do you find the average value of

Extrakt04

Extrakt04

Answered question

2022-06-16

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

Answer & Explanation

mallol3i

mallol3i

Beginner2022-06-17Added 20 answers

The formula for average value of a continuous function F(x) on [a,b] is
1 b a a b F ( x ) d x
Our formula here will be
A = 1 4 1 1 4 1 4 2 x d x
A = 1 3 1 4 2 x d x
A = 1 3 [ 2 x ln 2 ] 1 4
A = 1 3 [ 2 4 ln 2 2 1 ln 2 ]
A = 1 3 [ 14 ln 2 ]
A = 14 3 ln 2
This can be approximated as 6.7. The average value of y = 2 x on [1,4] is 6.7

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