Question

What is the average value of the function `F(x) = e ^ -x` on the interval `[0,4]`?

Answer 1

`1/4 (1 - 1/e^{4})`

Explanation:

graph{e^{-x}x^2 [-10, 10, -5, 5]}

by definition, `y_{ave} = (\int_a^b y \ dx )/(b-a)`

here `y_{ave} = (\int_0^4 e^{-x} \ dx )/(4-0)`

`= (1)/(4) [-e^{-x}]_0^4 = 1/4(-e^{-4} + 1) = 1/4 (1 - 1/e^{4})`