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integral calculus. n. 1. (Mathematics) 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, etc.Compare differential calculus.. (Mathematics) 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, etc. Compare differential calculus.
This result, while taught early in elementary calculus courses, is actually a very deep result connecting the purely algebraic indefinite integral and the purely analytic (or geometric) definite integral. Definite integrals may be evaluated in the Wolfram Language using Integrate[f, x, a, b]. The question of which definite integrals can be expressed in terms of elementary functions is not susceptible to any established theory. In fact, the problem belongs to transcendence theory, which appears to be infinitely hard..