the branch of mathematics that deals with integrals, especially the methods of ascertaining indefinite integrals and applying them to the solution of differential equations and the determining of areas, volumes, and lengths.

British Dictionary definitions for integral calculus

integral calculus

noun

the branch of calculus concerned with the determination of integrals and their application to the solution of differential equations, the determination of areas and volumes, etcCompare differential calculus

The study of integration and its uses, such as in calculating areas bounded by curves, volumes bounded by surfaces, and solutions to differential equations. Compare calculus of variationsdifferential calculus.