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The main theorem of differential and integral calculus: Differentiation is the opposite of integration. The statement is quite surprising at first. You can find an extended proof at http://www.slt.biz/Unterricht/2021/ht... You can find all my projects at http://www.slt.biz/Unterricht/gefilmt... In fact, the center of the proof is the consideration of an area difference and the establishment of a differential quotient.