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Basic integral question

  1. Jul 21, 2008 #1
    given f continuous on [a,b] with a not equal to b,
    [tex] \int{a_b}(f^2) = 0 [\tex]

    imply that f must be uniformly 0?

    (still not able to get Latex right, either. sorry)


  2. jcsd
  3. Jul 22, 2008 #2
    I don't know why they used 'f' since 'f' is generally used to be a function not describe them. If we change the f to x it makes this question easier.

    I don't know what it is saying when it asks is x is uniformly zero.
    If you find the definite integral of x^2 and make it equal to zero you get:
    a^3 = b^3

    Since a equals b there will never be any area under the curve. I'm sorry I don't know where to progress from here.
  4. Jul 22, 2008 #3
    Umm... What are you talking about? It seems fairly evident that f is representing a function.

    To krcmd1: What happens if f is not everywhere 0 on [a,b]?
  5. Jul 22, 2008 #4


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    If f is continuous then f2 is both continuous and non-negative. Suppose there were some point, say x0 at which f(x0[/sup]) is not 0. By continuity, you can find some small neighborhood of x0 in which f2 is positive. The integral of f2 over that neighborhood is positive. Since there are no negative values of f2 to cancel that, the integral of f2 [a, b] is larger than or equal to that positive number: it can't be 0.
  6. Jul 22, 2008 #5
    Thank you Halls of Ivy. That is just how I reasoned it. Don't have enough experience to be confident in my reasoning yet.

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