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Homework Help: Short question about integrals

  1. May 16, 2006 #1
    integral identity

    if we have [tex]\int dt f(t) = \int dt g(t) [/tex] where both integrals are indefinite integrals, can we immediately conclude that f(t) = g(t) ? I know this doesn't work with definite integrals.
     
    Last edited: May 16, 2006
  2. jcsd
  3. May 16, 2006 #2
    If the two integrals are equivalent, then this implies to me at every t the shapes of f(t) and g(t) are equivalent. It does not work with definite integrals because it's entirely possible for two functions to have the same integral over a certain interval but have entirely different shapes.
     
  4. May 16, 2006 #3

    CarlB

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    Homework Helper

    Write it out in complete for example:

    [tex]\int^xdt\;f(t) = \int^x dt\;g(t).[/tex]

    In other words, write the indefinite integrals as definite integrals. Now apply the fundamental theorem of calculus and you will find out that yes, indeed, f = g.

    Carl
     
  5. May 18, 2006 #4
    thanks! carl
     
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