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 differential dx usually follows to indicate x as the variable .) The basic rules of integration are: (1) ∫(f + g) d x = ∫ f d x + ∫ g d x (where f and g are functions of the variable x), (2) ∫ k f d x = k ∫ f d x (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 2 x is x 2 + 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 also differentiation .