Derivative of a definite integral?

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Main Question or Discussion Point

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
 

Answers and Replies

  • #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.
 
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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.
sorry. just integral, not definite integral
 
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SteamKing
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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.
Not necessarily.

You have to apply the Leibniz Rule:

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

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