For example, computation of the derivative could provide the instantaneous velocity of a moving particle; integration was useful in finding the area of curved regions. ... Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1800 BC), in which an Egyptian successfully calculated the volume of a pyramidal frustum. ... Around AD 1000, the Islamic mathematician Ibn al-Haytham (Alhazen) was the first to derive the formula for the sum of the fourth powers, and using mathematical induction, he developed a method that is...

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