A Rigorous Introduction to the Riemann Integral and the Fundamental Theorem of Calculus
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Summary
This article provides a rigorous mathematical introduction to the Riemann integral and proves the Fundamental Theorem of Calculus. It explains how the area under a curve can be approximated using rectangles via partition of the domain, and establishes the beautiful connection between integrals and derivatives. The content is academic and mathematical in nature, targeting readers with some calculus background.
Key quotes
· 3 pulledAlthough the notion of area is intuitive, its mathematical treatment requires a rigorous definition.
This post introduces the Riemann integral, and proves the fundamental theorem of calculus—a beautiful result that connects integrals and derivatives.
Given a bounded function f:[a,b]→R, we can approximate the area under its graph by rectangles.
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