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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.
Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide ...
The last expression is the logarithmic mean. = ( >) = (>) (the Gaussian integral) = (>) = (, >) (+) = (>)(+ +) = (>)= (>) (see Integral of a Gaussian function
The following is a list of integrals (antiderivative functions) of trigonometric functions.For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions.
The origins of differentiation likewise predate the fundamental theorem of calculus by hundreds of years; for example, in the fourteenth century the notions of continuity of functions and motion were studied by the Oxford Calculators and other scholars. The historical relevance of the fundamental theorem of calculus is not the ability to ...
Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity. Integrals involving only logarithmic functions
Fredholm: An integral equation is called a Fredholm integral equation if both of the limits of integration in all integrals are fixed and constant. [1] An example would be that the integral is taken over a fixed subset of . [3] Hence, the following two examples are Fredholm equations: [1]
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]