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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.
A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. [42] Various different line integrals are in use. In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field.
The fundamental theorem of calculus establishes the relationship between indefinite and definite integrals and introduces a technique for evaluating definite integrals. If the interval is infinite the definite integral is called an improper integral and defined by using appropriate limiting procedures. for example:
In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, ... Example. Let f(x, y) = 2 and
In addition to differential calculus and integral calculus, the term is also used for naming specific methods of computation or theories that imply some sort of computation. Examples of this usage include propositional calculus , Ricci calculus , calculus of variations , lambda calculus , sequent calculus , and process calculus .
The following is a list of integrals (antiderivative functions) ... However, it is conventional to omit this from the notation. For example, ...