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Homework Help: Question about Integration

  1. Jan 14, 2012 #1
    [itex]\int^{b}_{a}[/itex] f(x) dx = [itex]lim_{c → a^{+}}[/itex] [itex]lim_{d → b^{-}}[/itex] [itex]\int^{d}_{c}[/itex] f(x) dx

    Is this true?
     
  2. jcsd
  3. Jan 14, 2012 #2
    What are the arguments of the limit in this case?
     
  4. Jan 14, 2012 #3
    a and b on the left hand side and I replaced these with c and d evaluated with limits with a and b, a from the right and b from the left.
     
  5. Jan 14, 2012 #4
    Yes it always true, either if f(x) is continuos on [a,b] or on (a,b). In the first case you have a proper integral, in fact the primitive F(x) is also continuos and the limit is the value of F at a (or b). In the second case you have an improper integral and in that case is necessary to use the limit to check whether or not the result is a finite value.
     
  6. Jan 14, 2012 #5
    hmmm...
    ya i guess so thanks
     
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