How to Find the Average Value of a Function Over a Given Interval?

[KingKai]

Homework Statement

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

f(t) = (t²-1)e^-0.5t

Homework Equations

1/(b-a) ∫ f(x) = {f(x)}

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]

Homework Statement

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

f(t) = (t²-1)e^-0.5t

Homework Equations

1/(b-a) ∫ f(x) = {f(x)}

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.