The Fundamental theorem of Calculus Part 1 | Proof
Автор: John's Maths Book
Загружено: 2024-08-29
Просмотров: 464
Описание:
This video proves the first part of the fundamental theorem of calculus from first principles and shows that given a function f(t), the anti derivative F(x) when differentiated with respect to x equals f(x).
It starts with a function f(t) and shows points a and b on the t axis. The area F(x) under the curve is described between a and x on the t axis.
The mean value theorem for integrals is used to show that an area defined by F(x+h) - F(x) can be found by finding some value c where f(c) multiplied by h is the area.
The squeeze theorem is used to show that the limit of f(c) as h approaches zero equals f(x).
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