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Curated by: Mathemaniac (96 videos)
In this last video of this video series, we are going to investigate a bunch of ideas that fall within the umbrella of "Doing integrals without integration", including indefinite integrals, an elementary way to derive Cavalieri's quadrature formula, as well as complex analysis as a tool. Links: (1) Fundamental theorem of calculus: https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus (2) Quora answer (Cavalieri’s quadrature): https://www.quora.com/How-do-mathematicians-come-up-with-proofs-seemingly-out-of-nowhere-Can-I-come-up-with-my-own-unique-Proof-of-the-Power-Rule/answer/Dean-Rubine [which is based on Wildberger, N. J. (2002). "A new proof of Cavalieri's quadrature formula". The American Mathematical Monthly. 109 (9): 843–845. doi:10.2307/3072373. JSTOR 3072373.] (3) Complex analysis (HLMA - a high school student academic research competition): https://www.youtube.com/watch?v=8QiW6FSGUnE&list=PLKJV8qXE3Zwx9gAWBIDUOfgV0LbWC6wr_&index=4 Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video!