The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most beautiful equations in mathematics. It serves as the backbone of calculus and links its two main ideas: the concept of integral and the concept of derivative.

In mathematical language, the theorem states that the net change of a smooth and continuous quantity, such as a distance traveled, over a certain time interval is equal to the integral of its rate of change at each specific instance, or in other words, it is equal to the integral of its velocity. This remarkable theorem marks great progress in understanding how quantities can be measured over time – incredibly important in almost every area.

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