What does the integral symbol mean?
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).
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.
- 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.
- Historically, calculus was framed in terms of infinitesimally small numbers. The Leibniz notation dy/dx was originally intended to mean, literally, the division of two infinitesimals. The Leibniz notation ∫ f d x was meant to indicate a sum of infinitely many rectangles, each with infinitesimal width dx.
- The first part of the theorem, sometimes called the first fundamental theorem of calculus, states that one of the antiderivatives (also called indefinite integral), say F, of some function f may be obtained as the integral of f with a variable bound of integration.
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.
- Definition of solenoid. : a coil of wire usually in cylindrical form that when carrying a current acts like a magnet so that a movable core is drawn into the coil when a current flows and that is used especially as a switch or control for a mechanical device (such as a valve)
- Definition 2.4. A vector field F is called irrotational if it satisfies curl F = 0. The terminology comes from the physical interpretation of the curl. If F is the velocity field of a fluid, then curl F measures in some sense the tendency of the fluid to rotate.
- Irrotational flow is a flow in which each element of the moving fluid undergoes no net rotation with respect to a chosen coordinate axes from one instant to other. A well-known example of irrotational motion is that of the carriages of the Ferris wheel (giant wheel).
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 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. If a function has an integral, it is said to be integrable.
- This theorem is so important and widely used that it's called the “fundamental theorem of calculus”, and it ties together the integral (area under a function) with the antiderivative (opposite of the derivative) so tightly that the two words are essentially interchangeable.
- 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: 21st October 2019