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Average value

  1. Apr 21, 2004 #1
    Hmmm.... got this one wrong

    What is the average value of [tex] y = x^{2}\sqrt{x^3+1} [/tex] on the interval [0,2] ?

    Okay, so another average value problem right?

    [tex] f(b) - f(a) = f'(c)(b-a) [/tex]
    [tex] f(2) - f(0) = 2f'(c) [/tex]
    [tex] 12 = 2f'(c) [/tex]
    So then the average value is 6 right?
     
  2. jcsd
  3. Apr 21, 2004 #2

    jamesrc

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    Science Advisor
    Gold Member

    Your problem is that you're trying to find the average value of a function using the mean value theorem. Try using the definition of the average value of a function:

    [tex] \bar y = \frac{\int_a^b{f(x)dx}}{b-a} = \frac 1 2 \int_0^2{x^2\sqrt{x^3+1}dx} [/tex]

    (Simple change in variable to solve from here.)
     
  4. Apr 23, 2004 #3
    Simple use the following to find the Average Value of a function:

    1\b-a[tex] \int_a^b{f(x)dx} [/tex]
     
    Last edited: Apr 23, 2004
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