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Newton Leibnitz Formula for Evaluating Definite Integrals

  1. Mar 3, 2015 #1
    Lately, I have been trying really hard to understand the Newton Leibnitz Formula for evaluating Definite Integrals. It states that-
    If f(x) is continuous in [a,b] then [itex] \int_a^b f(x) dx = F(b) - F(a)[/itex].
    But one thing that just doesn't make sense to me is that why should f(x) be continuous in [a,b] if we need to apply this formula?
    Reply soon!
     
    Last edited: Mar 3, 2015
  2. jcsd
  3. Mar 3, 2015 #2
    Anybody there?
     
  4. Mar 3, 2015 #3
    do you know limit as as sum formula?
     
  5. Mar 3, 2015 #4

    HallsofIvy

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    It doesn't say that. The statement "if a then b" means "if a is true then b is true". It does NOT say anything about what happens if the hypothesis is NOT true.

    This theorem says that "if f is continuous on the interval [a, b], then [itex]\int_a^b f(t)dt= F(b)- F(a)[/itex]". It does NOT say anything about what happens if f is NOT continuous, If f is not continuous, then this may or may not be true.
     
  6. Mar 3, 2015 #5
  7. Mar 4, 2015 #6
    please read this-http://www3.ul.ie/~mlc/support/Loughborough%20website/chap15/15_1.pdf
     
  8. Mar 4, 2015 #7
    read it fully and pay attention to the formula of the area.
     
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