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Numerical integration has roots in the geometrical problem of finding a square with the same area as a given plane figure (quadrature or squaring), as in the quadrature of the circle. The term is also sometimes used to describe the numerical solution of differential equations.
Integral equation. For equations of integer unknowns, see Diophantine equation. In mathematics, integral equations are equations in which an unknown function appears under an integral sign. [1] In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u.
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. Integration was initially used to solve problems in mathematics and ...
The definite integral inputs a function and outputs a number, which gives the algebraic sum of areas between the graph of the input and the x-axis. The technical definition of the definite integral involves the limit of a sum of areas of rectangles, called a Riemann sum. [47]: 282 A motivating example is the distance traveled in a given time.
Calculus. In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards."
Also called resource cost advantage. The ability of a party (whether an individual, firm, or country) to produce a greater quantity of a good, product, or service than competitors using the same amount of resources. absorption The total demand for all final marketed goods and services by all economic agents resident in an economy, regardless of the origin of the goods and services themselves ...
Limits of integration. In calculus and mathematical analysis the limits of integration (or bounds of integration) of the integral. of a Riemann integrable function defined on a closed and bounded interval are the real numbers and , in which is called the lower limit and the upper limit. The region that is bounded can be seen as the area inside ...
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...