In this video, I give the classical proof of the fundamental theorem of calculus, the version which says that the derivative of the integral is just the function itself (this is sometimes called FTC 1). There are some epsilon-deltas involved, but not too much. Check out my other FTC video if you want to see a clever proof of the other version :)
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Proof of the Fundamental Theorem of Calculus (the one with differentiation)
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