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arXiv · 2402.14564

The Fundamental Theorem of Calculus in higher dimensions

Filip Bár
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Abstract

We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$ generalising the classical case. The generalised Fundamental Theorem of Calculus then states that the $n$-dimensional integrals over $n$-dimensional axis-parallel rectangular hypercuboids is given by a combinatorial formula evaluating the antiderivative on the vertices of the hypercuboid.

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Filip Bár. 2024-02-22. The Fundamental Theorem of Calculus in higher dimensions. https://arxiv.org/abs/2402.14564

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