Answer to Question #251135 in Calculus for bri

Question

Identify a mathematician that contributed to the development of theory of functions in Mathematics. State the contribution made and why was it so important to the field of Mathematics.

Answer 1

For examle, Isaac Newton, who in 1660s started working on the concept of integral and differential, which gave rise to the mathematical analysis. Famous Newton-Leibniz formula(to be fair, both Leibniz and Newton developed this concept approximately at the same time and independent from each other):

$\intop$ _a^b$f(x)dx=F(b)-F(a) = F(x)|$_a^b

where a, b are integration boundaries, dx is a differential, F(x) is the antiderivative function of f(x).

This formula allows to calculate the volume if the curved trapezoid is between f(x) and y = 0.

This formula gave powerful instrument to calculate the values of the function of the displacement with a help of the speed, mass with a help of the density etc. This is very helpful under the situatuion of irregularity of f(x) because before this formula there were only methods of approximate calculations, which were less accurate and took more time. This formula is being commonly used now for more than 300 years.