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Average Value of a Function

by KingKai
Tags: average, function
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KingKai
#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
#2
Dec5-12, 01:00 AM
P: 2,944
so to get the average of the function you integrate the function and then divide by the interval length.
vela
#3
Dec5-12, 01:01 AM
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Thanks
PF Gold
P: 11,726
Try a different technique.

SammyS
#4
Dec5-12, 09:49 AM
Emeritus
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PF Gold
P: 7,808
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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