The discussion revolves around finding the average value of the function f(t) = (t² - 1)e^(-0.5t) over the interval [0, 6]. Participants are exploring the application of integration techniques to solve this problem.
The discussion is ongoing, with participants sharing their attempts and suggesting alternative methods. There is no explicit consensus on the approach to take, but several lines of reasoning are being explored.
Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply.
Use integration by parts, twice.KingKai said: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.