How do you find the average value of the function for f ( x )...

Maliyah Robles

Maliyah Robles

Answered

2022-07-03

How do you find the average value of the function for f ( x ) = e x , 1 x 1?

Answer & Explanation

Miguidi4y

Miguidi4y

Expert

2022-07-04Added 13 answers

Explanation:
By definition, the average value of a function f(x) over a domain [a,b] is given by:
f ( x ) = 1 b a a b f ( x ) d x
So, for the given function, f ( x ) = e x with 1 x 1, we have:
f ( x ) = 1 1 ( 1 ) 1 1 e x d x
= 1 2 [ e x ] 1 1
= 1 2 ( e e 1 )
= 1 2 ( e 1 e )
1.1752

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