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Math Help - From Riemanns sum to definite integral

  1. #1
    Boo
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    From Riemanns sum to definite integral

    Dear All!
    I found this as an explanation!

    Definite Integral Proof? - Yahoo! Answers

    The problem is that I just dont understand it still form the first line:
    F(X1) F(a) = F(C1) * (X1-a) = F(C1)*ΔX1 = f(C1)* ΔX1

    Please, how do we get this?
    Many thanks!!!
    p.s. please, don't be angry I ask too much!!!
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  2. #2
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    Re: From Riemanns sum to definite integral

    Quote Originally Posted by Boo View Post
    Dear All!
    I found this as an explanation!
    Definite Integral Proof? - Yahoo! Answers
    The problem is that I just dont understand it still form the first line:
    F(X1) F(a) = F(C1) * (X1-a) = F(C1)*ΔX1 = f(C1)* ΔX1
    Please, how do we get this?
    Many thanks!!!
    p.s. please, don't be angry I ask too much!!!
    I do not think that anyone will be angry, certainly not me, at your question.
    However, I will tell that I have given a semester long course on the theory of the integral in an attempt to completely answer your question.
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  3. #3
    Boo
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    Re: From Riemanns sum to definite integral

    Can someone give me the hint?
    Everyone I know avoids to answer....
    What is C_1???
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  4. #4
    MHF Contributor

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    Re: From Riemanns sum to definite integral

    Quote Originally Posted by Boo View Post
    Dear All!
    I found this as an explanation!

    Definite Integral Proof? - Yahoo! Answers

    The problem is that I just dont understand it still form the first line:
    F(X1) F(a) = F(C1) * (X1-a) = F(C1)*ΔX1 = f(C1)* ΔX1
    C1 is a point chosen so that F(X1) F(a) = F(C1) * (X1-a). The fact that there exist such a value, C1, follows from the "mean value theorem". The fact that those equal F'(C1)*ΔX1 is just that ΔX1 is defined as (X1- a). And the fact that F'(C1)ΔX1= f(C1) follows from the fact "f" is defined as F'.

    Please, how do we get this?
    Many thanks!!!
    p.s. please, don't be angry I ask too much!!![/QUOTE]
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