Use the Fundamental Theorem of Calculus to find the average value of f(x)=e^0.4x between x=0 and x=2.

Question

Find the average value on the graph. Finally give the exact x value for which f(x)=the average value.
Answer for the x value: ?

I keep getting 40ln(20e^0.8-20) and it is wrong.

Answer 1

from my sketch it would be
∫ e^.4x dx from 0 to 2
= [ (1/.4) e^.4x dx from 0 to 2
= (1/.4) e^(.4)(2) - (1/.4) e^0
= 2.5( e^.8 - 1)
= appr 3.064

Answer 2

How does ln possibly enter the picture in your answer ?

Answer 3

the average value is 1/2 the area above