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Second fundamental theorem of calculus viewed as a transform?

  1. Nov 6, 2012 #1
    You see this picture of the second fundamental theorem of calculus 32e174d296c019dcd366191d117c3385.png and you are taught in high school / early college calculus that the t is a dummy variable. However, couldn't you view this as some sort of transform? You convert a function f(t) into a function of f(x). Is this a valid way to view this fundamental theorem of calculus?

    Thanks,

    Vanmaiden
     

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  2. jcsd
  3. Nov 6, 2012 #2

    lurflurf

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    Homework Helper

    Yes the theorem is that two transforms are inverse
    [tex]DF=\lim{h\rightarrow 0} \frac{F(x+h)-F(x)}{h}[/tex]
    [tex]If=\int_a^x f(t) dt[/tex]

    The fundamental theorem is that
    IDF=F
    and
    DIf=f
    which is not obvious
     
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