Applications of Line Integral
As already mentioned, a Line Integral is used to find a function’s integral along a line or a curve. Here, some practical applications of line integrals are listed as follows:
- It may be used in finding work done by gravitational force to move a particle along a specific path defined by a curve.
- It can be used in finding work done by a force on a moving object.
- It is used in determining rate of reaction as per Law of Mass Action.
- It is also used to calculate the value of magnetic field around a conductor as per Ampere’s Law.
- It is also used to find the voltage generated in a loop due to electromagnetic induction as per Faraday’s Law.
There are many more applications of Line Integrals which one may find in various engineering fields. Below are some solved examples which are involve calculation of line integral. You may refer them to understand the concept of line integral in a better way.
Line Integral
Line Integral is the integral that is evaluated along a line or a curve. Generally, an integral is calculated when we need to determine a quantity’s value such as area, volume, temperature, etc. for a larger part of the body when we have an expression for a smaller part. It is the opposite of differentiation and is also called an anti-derivative of the function. The Line Integral is used in engineering in various fields when we need to determine a function’s value along a line or along a curve. For example, if we need to calculate work done on an electron by a force field along a curve, we can determine it using line integral.
In this article, we will learn about the definition of line integral, its formula of line Integral, applications of line Integral, some solved examples based on the calculation of line integral, and some frequently asked questions related to line integral.
Table of Content
- Definition of Line Integral
- Formula of Line Integral
- For scalar Fields
- For Vector Fields
- Line Integral in Differential Form
- Evaluating Line Integral
- Fundamental Theorem for Line Integrals
- Applications of Line Integral
- Line Integrals of Vector Valued Functions
- Examples on Line Integral