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Improper integrals

  1. Oct 8, 2008 #1
    1. The problem statement, all variables and given/known data
    -∞
    ∫f(t)dt
    a

    b
    ∫f(t)dt
    -∞

    b
    ∫f(t)dt
    a

    Now add the first two integrals, do we get the third integral?
    2. Relevant equations
    N/A


    3. The attempt at a solution
    Suppose we have

    c
    ∫f(t)dt
    a

    b
    ∫f(t)dt
    c

    b
    ∫f(t)dt
    a

    Then adding the first two integrals will give the third integral, but what happens in the case of improper integrals?
     
  2. jcsd
  3. Oct 8, 2008 #2
    this would hold, i assume, if
    -∞
    ∫f(t)dt
    a

    b
    ∫f(t)dt
    -∞


    would converge.
     
  4. Oct 9, 2008 #3
    So the property [​IMG] holds also for improper integrals?
     
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