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In calculus, the process of finding a function whose derivative is a given function. The term, sometimes used interchangeably with antidifferentiation, is indicated symbolically with the integral sign . (The differentialdx usually follows to indicate x as the variable.) The basic rules of integration are: (1) (f + g)dx = fdx + gdx (where f and g are functions of the variable x), (2) kfdx = kfdx (k is a constant), and (3) (C is a constant). Note that any constant value may be added onto an indefinite integral without changing its derivative. Thus, the indefinite integral of 2x is x2 + C, where C can be any real number. A definite integral is an indefinite integral evaluated over an interval. The result is not affected by the choice for the value of C. See alsodifferentiation.
This entry comes from Encyclopædia Britannica Concise. For the full entry on integration, visit Britannica.com.