# What is an integral in calculus?

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**.A.

### 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).#### What does the definite integral?

with , , and in general being complex numbers and the path of**integration**from to known as a contour. The first fundamental theorem of calculus allows**definite integrals**to be computed in terms of**indefinite integrals**, since if is the**indefinite integral**for a continuous function , then.#### Is an integral an Antiderivative?

The notation used to refer to**antiderivatives**is the indefinite**integral**. f (x)dx means the**antiderivative**of f with respect to x. If F is an**antiderivative**of f, we can write f (x)dx = F + c. In this context, c is called the constant of integration.#### Is a derivative?

A**derivative**is a contract between two or more parties whose value is based on an agreed-upon underlying financial asset (like a security) or set of assets (like an index). Common underlying instruments include bonds, commodities, currencies, interest rates, market indexes and stocks.

B.

### What is an integral symbol?

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.#### What is the fundamental theorem of calculus?

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.#### What is the name of the integral sign?

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.#### What does the integral do?

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**.

C.

### 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.#### What is curl F?

In vector calculus, the**curl**is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space. At every point in the field, the**curl**of that point is represented by a vector. The**curl**is a form of differentiation for vector fields.#### What is the meaning of Solenoidal?

**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)#### Is the magnetic field conservative?

The**magnetic field**itself is neither**conservative**nor non-**conservative**.**Magnetic field**lines do go in closed paths but that's not the definition of**conservative**. Rather, a**field**is**conservative**when the force on a test particle moving around any closed path does no net work.

Updated: 9th October 2018