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Posted by on Thursday, October 29, 2009 at 9:07pm.

f(t)= -2te^-t^2, [0,5] Find average value.
Attempt: I know that the average value is the integration of f(t) from a to b divided by b-a. I used u substitution to get u= -t^2 and du= -2xdx. I
changed the limits of integration to [0,25] and I got integral of e^u du.
I am not sure if this is right, but then would the integral of that be
just e^u and I would just plug in 25, because I did that and the answer
was wrong.

  • Calculus - , Thursday, October 29, 2009 at 9:39pm

    I don't see anything wrong with your approach. Perhaps there was an arithmetic error lurking somewhere.
    What did you get for the answer?
    Did you divide the integral by 5 or 25?

  • Calculus - , Friday, October 30, 2009 at 4:25pm

    You are almost right but since u=-t^(2) the limits are [0,-25] then put them into e^(u) and you get,

    e^(-25)-e^(0)=
    e^(-25)-1

    Then divide that answer by 5 thus the answer is,

    (e^(-25)-1)/5

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