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Hello all, new poster here.

When learning about the definition of the definite integral, a few books that I have read through first define anitdifferentiation, then explains some Riemann sums and then

POOF

[tex]\int_{a}^{b} f(x) dx = \lim_{||\Delta||\rightarrow\0}\sum_{i=1}^n f(\xi_i) \Delta_i x[/tex]

So is there a proof for this or do I just gotta accept it? Please help with the integral definition.

When learning about the definition of the definite integral, a few books that I have read through first define anitdifferentiation, then explains some Riemann sums and then

POOF

[tex]\int_{a}^{b} f(x) dx = \lim_{||\Delta||\rightarrow\0}\sum_{i=1}^n f(\xi_i) \Delta_i x[/tex]

So is there a proof for this or do I just gotta accept it? Please help with the integral definition.

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