To try everything Brilliant has to offer—free—for a full 30 days, visit . You’ll also get 20% off an annual premium subscription. The Riemann Integral was developed as a way to calculate the area under a curve. Then came a function that was impossible to integrate. This dilemma would lead one mathematician, Henri Lebesgue, to invent an entirely new approach. The Lebesgue Theory of Integration was a much better theory of integration and it would ultimately change the way we think about the integral forever. _____ Join my Patreon community: Support the channel with a one-time donation: _____ Video on the Vitali Set: What is a Hilbert Space? What is a Banach Space? _____ Article on the Lebesgue Integral: Music: Epidemic Sound Animations created using Manim: Illustrations and Thumbnails: Christine Kosakowski This video was sponsored by Brilliant