## What is the line integral of a vector field?

## What is the line integral of a vector field?

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.

## What are line and surface integrals explain them with examples?

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. It can be thought of as the double integral analog of the line integral.

**Which of the following is an example of vector field?**

A gravitational field generated by any massive object is also a vector field. For example, the gravitational field vectors for a spherically symmetric body would all point towards the sphere’s center with the magnitude of the vectors reducing as radial distance from the body increases.

**How do you do line integrals?**

This is red curve is the curve in which the line integral is performed….Definition of a Line Integral.

requirement | simple integrals | For line integrals |
---|---|---|

2 | the equation of the path in parametric form (x(t),y(t)) | |

3 | bounds in terms of x=a and x=b | the bounds in terms of t=a and t=b |

### What do line integrals represent?

A line integral allows for the calculation of the area of a surface in three dimensions. Line integrals have a variety of applications. For example, in electromagnetics, they can be used to calculate the work done on a charged particle traveling along some curve in a force field represented by a vector field.

### What is the difference between line integral and double integral?

Our main objects of study will be two types of integrals: Double integrals, which are integrals over planar regions. Line or path integrals, which are integrals over curves.

**What is the difference between definite and line integral?**

Line integrals has a continuously varying value along that line. Definite integrals express as the difference between the value of the integral at specified appear and lower limit of the independent variable.