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Proof of Anti-differentiation

  1. May 13, 2015 #1
    While attempting proof for Integration is anti-differentiation from the book Mathematical methods for physics, Riley, Hobson
    How the R.H.S of the equation (after rearranging and dividing by Λx) becomes f(x)Λx?
     

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  3. May 13, 2015 #2

    Svein

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    Well, the (Riemann) integral from a to b is defined as the upper limit of [itex]\sum_{\bigcup \Delta x = [a, b]}f(x)\cdot\Delta x [/itex]. So, if you put a=x and b=x+Δx, you get the first element in the sum. Which means that [itex]\int_{x}^{x+\Delta x}f(x)dx [/itex] is the upper limit of [itex]f(x)\cdot \Delta x[/itex] (as Δx→0).
     
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