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  2. Antiderivative - Wikipedia

    en.wikipedia.org/wiki/Antiderivative

    The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.

  3. Constant of integration - Wikipedia

    en.wikipedia.org/wiki/Constant_of_integration

    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.

  4. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations.Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation.

  5. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. [46]: 508 The indefinite integral, also known as the antiderivative, is the inverse operation to the derivative.

  6. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/.../Fundamental_theorem_of_calculus

    The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions).

  7. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    Integration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...

  8. Integral symbol - Wikipedia

    en.wikipedia.org/wiki/Integral_symbol

    The integral symbol (see below) is used to denote integrals and antiderivatives in mathematics, especially in calculus. ∫ ( Unicode ), ∫ {\displaystyle \displaystyle \int } ( LaTeX ) History

  9. Integral of inverse functions - Wikipedia

    en.wikipedia.org/wiki/Integral_of_inverse_functions

    In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse of a continuous and invertible function, in terms of and an antiderivative of .

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