## Average Value of a Function

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.

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 so to get the average of the function you integrate the function and then divide by the interval length.
 Mentor Try a different technique.

Mentor

## Average Value of a Function

 Quote by 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.
Use integration by parts, twice.