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I Derivative of a definite integral?

  1. Apr 23, 2016 #1
    consider x is between the interval [a,b]
    would it be correct to say that the derivative of a definite integral F(x) is f(x) because as dx approaches zero in (x + dx), the width of ALL "imaginary rectangles" would closely resemble a line segment which approximates f(x)? therefore change in area under a curve is dependent to the change in the height of f(x) with respect to dx(which is inifinitesimally small)??

    the different notations used in several videos i watched seemed to have confused me or doubt my own understanding of a seemingly simple concept
     
  2. jcsd
  3. Apr 23, 2016 #2

    Math_QED

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    Derivative of a definite integral? The definite integral calculates an orientated area. This is a constant. The derivative of a constant equals zero. Therefor, the derivative of a definite integral is zero.
     
  4. Apr 23, 2016 #3
    sorry. just integral, not definite integral
     
  5. Apr 23, 2016 #4

    SteamKing

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    Not necessarily.

    You have to apply the Leibniz Rule:

    https://en.wikipedia.org/wiki/Leibniz_integral_rule
     
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