The First Fundamental Theorem Of Calculus with example through Riemann sum |
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Website: https://mymathsclub.com/ Email: maria@mymathsclub.com FB: https://web.facebook.com/mymathsclub786 (I'll be glad if you write your valuable reviews here as well) WhatsApp Group: https://chat.whatsapp.com/K0UqNIuhIkq82vWVQ4cRLe If you need to hire services for language tutoring, website designing, logo making, video animation, search engine optimization, and much more, then please click the following links, you’ll find qualitative and reliable services at reasonable rates; • Language tutoring: https://bit.ly/3kCzig2 • Fitness lessons: https://bit.ly/3sTVJ4p • Life Coaching: https://bit.ly/2V1VRSU • Website designing: https://bit.ly/3gCXLRt • Logo Making: https://bit.ly/2WDyTC9 • Video Animation: https://bit.ly/3yoZNuA • Search Engine Optimization (SEO): https://bit.ly/3sSKgSA • Social Media Marketing: https://bit.ly/3zsTSpE Geometrical interpretation of univariate function:- https://youtu.be/P_GUfd1OC1I Tangent line and derivatives:- https://youtu.be/TUvMnfb972g Second fundamental theorem of calculus:- https://youtu.be/lPjWIb18Y_s Please watch: "Limit of a function f(x): Epsilon ϵ and Delta δ definition with example" https://www.youtube.com/watch?v=yt_fh-TPeDk --~-- "THE FIRST FUNDAMENTAL THEOREM OF CALCULUS" HISTORY OF FUNDAMENTAL THEOREM OF CALCULUS:- The fundamental theorem of calculus relates differentiation and integration, showing that these two operations are essentially inverses of one another. Before the discovery of this theorem, it was not recognized that these two operations were related. Ancient Greek mathematicians knew how to compute area via infinitesimals, an operation that we would now call integration. The origins of differentiation likewise predate the Fundamental Theorem of Calculus by hundreds of years; for example, in the fourteenth century the notions of continuity of functions and motion were studied by the Oxford Calculators and other scholars. The historical relevance of the Fundamental Theorem of Calculus is not the ability to calculate these operations, but the realization that the two seemingly distinct operations (calculation of geometric areas, and calculation of velocities) are actually closely related. The first published statement and proof of a rudimentary form of the fundamental theorem, strongly geometric in character, was by James Gregory (1638–1675), Isaac Barrow (1630–1677) proved a more generalized version of the theorem, while his student Isaac Newton (1642–1727) completed the development of the surrounding mathematical theory. Gottfried Leibniz (1646–1716) systematized the knowledge into a calculus for infinitesimal quantities and introduced the notation used today. |