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Average Value

  1. Feb 25, 2004 #1
    I forgot the formula for the average value of a function.
    Is that [tex] f(b) - f(a) = f'(c)(b-a) [/tex] or am I thinking of something else?
  2. jcsd
  3. Feb 25, 2004 #2

    [tex]\frac{\int_a^b f(x)\,dx}{b-a}}[/tex]

    Just remember that you're turning the area under the curve into a rectangle of base (b - a). The height is the average value.

  4. Feb 25, 2004 #3
    okay, the actual problem now becomes
    [tex] \frac{\int_{-1}^{1} e^{-x^2} \,dx}{-2} [/tex]
    any takers?
  5. Feb 25, 2004 #4
    You've got an extra negative in the denominator.

    The expression can be simplified at most to:

    [tex]\int_0^1 e^{-x^2}\,dx[/tex]

    Which must be integrated numerically. Mathematica gives:

    [tex]\int_0^1 e^{-x^2}\,dx = .746824[/tex]

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