Evaluating Line Integral
Line Integral can be evaluated using the formulae defined above for a particular problem depending upon whether it is for scalar field or vector field. The basic steps involved in evaluating line integral are listed as follows:
- As a first step, we need to parameterize the curve along which integral is to be found out in specified range, if not given in that form already.
- Find the differentials for the parametric curve obtained, as dx, dy and dz.
- Select the appropriate formula based upon scalar or vector fields.
- Substitute the parametric function and it’s derivative into the formula.
- Evaluate the dot product for vector fields or simply multiply for scalar ones.
- Integrate the obtained expression within specified limits to get the value of line integral.
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