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Homework Help: Evaluating a definite integral when a condition is given

  1. Jun 2, 2013 #1
    1. The problem statement, all variables and given/known data
    Given that x[itex]^{2}[/itex]f(x)+f([itex]\frac{1}{x}[/itex])=0, then evaluate [itex]\int[/itex][itex]^{1.5}_{0.6}[/itex]f(x)dx

    2. Relevant equations

    3. The attempt at a solution

    tried to replace f(x) using the provided equation...didn't help
  2. jcsd
  3. Jun 3, 2013 #2


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    Can you elaborate on how you tried replacing f(x)?
  4. Jun 3, 2013 #3


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    Have you looked at what happens if you substitute y = 1/x in the integral and the use the equation to substitute for f(1/y)?
    (Are you sure you've quoted the bounds correctly? It's not from a lower bound of 0.66666... by any chance?)
  5. Jun 5, 2013 #4
    well If I do that I shall be returning to the same problem statement...
  6. Jun 5, 2013 #5

    Ray Vickson

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    If the lower limit in the integral is 0.6, you cannot answer the question without knowing more about the function f(x). If the lower limit is 0.6666.... = 2/3, you can answer the question without knowing more about f(x).

    The substitution u = 1/x DOES work if you do it judiciously!
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