Posted by Will on Tuesday, January 26, 2010 at 12:13am.
Calculate he average over the given interval: f(x)=e^(n*x), [1,1].
I know that the average value = (1/ba)integrate from a to b f(x)dx

calculus  drwls, Tuesday, January 26, 2010 at 12:31am
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.

calculus  Will, Tuesday, January 26, 2010 at 12:45am
thanks, but can we leave it in that form?

calculus  drwls, Tuesday, January 26, 2010 at 10:03am
You can convert my answer to a hyperbolic sine of n, divided by 2, if you wish.

calculus  drwls, Tuesday, January 26, 2010 at 10:03am
I meant "divided by n", not 2

calculus  Will, Tuesday, January 26, 2010 at 7:06pm
What is hyperbolic sin of n? Never heard of that.
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