Question

find the average value of the function over the given interval.

f(x)=e^-2x , [0,4]

Answer 1

the average value of the function = ((4)-f(0) )/(4-0) = (e^-8 -8 -1)/4 =
\[[ e^{-8}-9]/4\]

Answer 2

http://archives.math.utk.edu/visual.calculus/5/average.1/index.html
\[Averavge = [\int\limits_{0}^{4}e ^{-2x} dx]/4\]
\[= (1/4)*[(-1/2)e ^{-2x}]from 0~ \to 4\]
= (-1/8)((1/e^8) - 1)
\[= 1/8 - 1/(8e ^{8})\]

Answer 3

sorry back of the book said [1-(e^-8)]/8

Answer 4

That is my answer.