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A line integral (sometimes called a path integral) is the integral of some function along a curve. One can integrate a scalar-valued function along a curve, obtaining for example, the mass of a wire from its density. One can also integrate a certain type of vector-valued functions along a curve.

The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.

Definition: Line Integrals. Let f be a function defined on a curve C of finite length. Then the line integral of f along C is. ∫Cf(x,y)ds=limn→∞n∑i=1f(xi,yi)Δsi.

The process of finding the antiderivative of the function is known as integration of the function. The standard form of indefinite integral is ∫f(x)dx, whereas the standard form of definite integral is ∫baf(x)dx, where a,b are lower and upper limits.

A line integral is an integral where the function to be integrated is evaluated along a curve and a surface integral is a generalization of multiple integrals to integration over surfaces.

One interpretation of the line integral of a vector field is the amount of work that a force field does on a particle as it moves along a curve.

Line integral of a scalar field The line integral over a scalar field f can be thought of as the area under the curve C along a surface z = f(x,y), described by the field.

There are two types of line integrals: scalar line integrals and vector line integrals. Scalar line integrals are integrals of a scalar function over a curve in a plane or in space. Vector line integrals are integrals of a vector field over a curve in a plane or in space.

A line integral (sometimes called a path integral) is the integral of some function along a curve. One can integrate a scalar-valued function along a curve, obtaining for example, the mass of a wire from its density. One can also integrate a certain type of vector-valued functions along a curve.

The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.

Definition: Line Integrals. Let f be a function defined on a curve C of finite length. Then the line integral of f along C is. ∫Cf(x,y)ds=limn→∞n∑i=1f(xi,yi)Δsi.

The process of finding the antiderivative of the function is known as integration of the function. The standard form of indefinite integral is ∫f(x)dx, whereas the standard form of definite integral is ∫baf(x)dx, where a,b are lower and upper limits.

A line integral is an integral where the function to be integrated is evaluated along a curve and a surface integral is a generalization of multiple integrals to integration over surfaces.

One interpretation of the line integral of a vector field is the amount of work that a force field does on a particle as it moves along a curve.

Line integral of a scalar field The line integral over a scalar field f can be thought of as the area under the curve C along a surface z = f(x,y), described by the field.

There are two types of line integrals: scalar line integrals and vector line integrals. Scalar line integrals are integrals of a scalar function over a curve in a plane or in space. Vector line integrals are integrals of a vector field over a curve in a plane or in space.