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Posted by 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/b-a)integrate from a to b f(x)dx

  • calculus - , 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 - , Tuesday, January 26, 2010 at 12:45am

    thanks, but can we leave it in that form?

  • calculus - , 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 - , Tuesday, January 26, 2010 at 10:03am

    I meant "divided by n", not 2

  • calculus - , Tuesday, January 26, 2010 at 7:06pm

    What is hyperbolic sin of n? Never heard of that.

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