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In calculus, the constant of integration, often denoted by (or ), is a constant term added to an antiderivative of a function () to indicate that the indefinite integral of () (i.e., the set of all antiderivatives of ()), on a connected domain, is only defined up to an additive constant.
Suppose a and b are constant, and that f(x) involves a parameter α which is constant in the integration but may vary to form different integrals. Assume that f ( x , α ) is a continuous function of x and α in the compact set {( x , α ) : α 0 ≤ α ≤ α 1 and a ≤ x ≤ b }, and that the partial derivative f α ( x , α ) exists and is ...
Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.
A constant (the constant of integration) ... is the Euler–Mascheroni constant which equals the value of a number of definite integrals. Finally, ...
Integration was first rigorously formalized, using limits, by Riemann. [13] ... as M(b − a) is the integral of the constant function with value M over [a, b]. In ...
Many of the following antiderivatives have a term of the form ln |ax + b|.Because this is undefined when x = −b / a, the most general form of the antiderivative replaces the constant of integration with a locally constant function. [1]
Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity. Integrals involving only logarithmic functions
constant of integration The indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration. [15] [16] This constant expresses an ambiguity inherent