Asked by Will
Calculate he average over the given interval: f(x)=e^(-n*x), [-1,1].
I know that the average value = (1/b-a)integrate from a to b f(x)dx
I know that the average value = (1/b-a)integrate from a to b f(x)dx
Answers
Answered by
drwls
You have stated the definition of the average value correctly. All you have to do is perform the integration and divide the integral by the integration interval, 2.
The indefinite integral of e^(-nx) is (-1/n)*e^(-nx).
The definite integral from -1 to 1 is
(-1/n)[e^-n - e^n]
Divide that by 2 for the average value.
Check my math. I am often sloppy.
The indefinite integral of e^(-nx) is (-1/n)*e^(-nx).
The definite integral from -1 to 1 is
(-1/n)[e^-n - e^n]
Divide that by 2 for the average value.
Check my math. I am often sloppy.
Answered by
Will
thanks, but can we leave it in that form?
Answered by
drwls
You can convert my answer to a hyperbolic sine of n, divided by 2, if you wish.
Answered by
drwls
I meant "divided by n", not 2
Answered by
Will
What is hyperbolic sin of n? Never heard of that.
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