3rd century BC - Archimedes develops a concept of the indivisibles—a precursor to infinitesimals—allowing him to solve several problems using methods now termed as integral calculus. Archimedes also derives several formulae for determining the area and volume of various solids including sphere, cone, paraboloid and hyperboloid.[2]
Before 50 BC - Babylonian cuneiform tablets show use of the Trapezoid rule to calculate of the position of Jupiter.[3]
3rd century - Liu Hui rediscovers the method of exhaustion in order to find the area of a circle.
14th century - Madhava discovers the power series expansion for , , and [6][7] This theory is now well known in the Western world as the Taylor series or infinite series.[8]
14th century - Parameshvara discovers a third order Taylor interpolation for ,
1811 - Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration,
1815 - Siméon Denis Poisson carries out integrations along paths in the complex plane,
1831 - Mikhail Vasilievich Ostrogradsky rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green,
1908 - Josip Plemelj solves the Riemann problem about the existence of a differential equation with a given monodromic group and uses Sokhotsky - Plemelj formulae,