What is integral line?
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour integral as well, although that is typically reserved for line integrals in the complex plane.
The integral sign ∫ represents integration. The symbol dx, called the differential of the variable x, indicates that the variable of integration is x. The function f(x) to be integrated is called the integrand. The symbol dx is separated from the integrand by a space (as shown).
- Finding the integral of a function with respect to x means finding the area to the x axis from the curve. The integral is usually called the anti-derivative, because integrating is the reverse process of differentiating. The fundamental theorem of calculus shows that antidifferentiation is the same as integration.
- Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts.
- History of calculus or infinitesimal calculus, is a history of a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Isaac Newton and Gottfried Leibniz independently invented calculus in the mid-17th century.
That is, it's usually called the "integral symbol". For its origins: "∫ symbol is used to denote the integral in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz towards the end of the 17th century.
- Contour integration is the process of calculating the values of a contour integral around a given contour in the complex plane. "Applications to the Calculation of Definite Integrals and Sums." §4.5 in Handbook of Complex Variables.
- In mathematics, the derivative is a way to show rate of change: that is, the amount by which a function is changing at one given point. For functions that act on the real numbers, it is the slope of the tangent line at a point on a graph.
- The Definition of Differentiation. The essence of calculus is the derivative. The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.
An integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. The Riemann integral is the simplest integral definition and the only one usually encountered in physics and elementary calculus.
- The integer is a whole number as opposed to a fraction such as 3, 6, 8, 15, 1284. Integral means consisting of a whole number or an undivided quantity. The term integral may also refer to the notion of antiderivative, a function F whose derivative is the given function f. The set of integers can be denoted by Z.
- Integration testing, also known as integration and testing (I&T), is a software development process which program units are combined and tested as groups in multiple ways. In this context, a unit is defined as the smallest testable part of an application.
- Integration occurs when separate people or things are brought together, like the integration of students from all of the district's elementary schools at the new middle school, or the integration of snowboarding on all ski slopes. You may know the word differentiate, meaning "set apart." Integrate is its opposite.
Updated: 9th October 2018