Integral and Differentiation — The fundamental theorem Part 2
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Integral and Differentiation — The fundamental theorem Part 2
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The culmination point of the podcast well-defined & wonderful (for now, anyway) is the second part of the fundamental theorem. It combines the most important notions of the podcast so far: continuity, differentiation, and integration. We shall show that continuous functions on bounded and closed intervals always admit an anti-derivative. This anti-derivative is given as the integral of this function integrated with a variable right end point. The first and second part of the fundamental theorem lead to the substitution rule and the integration by parts formula. Finally we will also attempt to prove the second part of the fundamental theorem by providing the main tricks and glueing them together into one wonderful proof.
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