Average Value of a Function


by KingKai
Tags: average, function
KingKai
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#1
Dec5-12, 12:57 AM
P: 31
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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jedishrfu
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#2
Dec5-12, 01:00 AM
P: 2,493
so to get the average of the function you integrate the function and then divide by the interval length.
vela
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#3
Dec5-12, 01:01 AM
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Thanks
PF Gold
P: 11,536
Try a different technique.

SammyS
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#4
Dec5-12, 09:49 AM
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Average Value of a Function


Quote Quote by KingKai View Post
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.


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