Home | 18.01 | Chapter 13 | Section 13.1

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Proof of the first fundamental theorem

We write f(b) - f(a) as the sum of the difference of f over many little intervals xk - xk-1

We apply the mean value theorem on each small interval

This yields, for some ck in the kth interval for each k.

This is a Riemann sum for integrand f '(x), limits a and b, and variable of integration x, for any n.

By taking the limit as , we get