Average Value of a Function

KingKai

1. The problem statement, all variables and given/known data

Determine the average value of the following function over the interval [0,6]

f(t) = (t²-1)e^-0.5t

2. Relevant equations

1/(b-a) ∫ f(x) = {f(x)}

3. The attempt at a solution

Substitution?

let u = (t²-1)

du/dt = 2t

du/2t = dt

1/(6) ∫ u e^-0.5t (du/2t)


And here, I reach a roadblock.

jedishrfu

so to get the average of the function you integrate the function and then divide by the interval length.

vela

Try a different technique.

SammyS

Use integration by parts, twice.