Integral and Differentiation — The fundamental theorem Part 1
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Integral and Differentiation — The fundamental theorem Part 1
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In this episode we are studying a first connection of differentiation and integration. More precisely, we will show that if a Riemann integrable function has an anti-derivative then the computation of the integral comes down to the evaluation of the anti-derivative. The proof provided uses a re-interpretation of the mean value theorem. A reorganisation of the terms involved in the statement of the mean value theorem leads to a relation of function evaluation and the integral of a step function with some height given by the derivative at some point of the function. A telescoping sum and a limit argument concludes the proof.
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