Types of Integration
Integration can be classified into three types:
Definite Integration
The integration with limits is called as the definite integration. The antiderivative p(x) of a continuous function f(x) on the interval [a, b] is known as definite integration. It is represented by and its value equals to p(b) – p(a) where p(b) is antiderivative at x = b and p(a) is the antiderivative at x = a. The a and b are called the limits of integration where a is the lower limit and b is the upper limit of integration. The interval [a, b] is called the interval of the integration. In the definite integration, the constant of integration is not required.
Learn more about Definite Integration.
Indefinite Integration
The integration with no limits is called the indefinite integration. In the indefinite integration, we add a constant with the result called the constant of integration. The integration of f(x) is given by:
∫f(x) dx = P(x) + C
Where,
- x is the variable of integration,
- f(x) is integrand,
- P(x) is antiderivative of f(x), and
- C is constant of Integration.
Improper Integration
The integration whose integrand is not bounded, or the limit of the integral is infinity, then the integration is called as improper integration. Some examples of improper integrations are: [Tex]\int\limits_1^\infty [/Tex]f(x)dx or [Tex]\int\limits_0^1 [/Tex](dx / x)
Integration
Integration is an important part of calculus. It involves finding the anti-derivative of a function and is used to solve integrals. Integration has numerous applications in various fields, such as mathematics, physics, and engineering.
This article serves as a comprehensive guide to integration, covering everything from integration formulas to methods for finding integrals. It also explains the properties and real-world applications of integration through solved examples. Let’s start exploring the topic of Integration.
Table of Content
- What is Integration?
- Integration Definition
- Integration Symbol
- Rules for Integration
- Power Rule of Integration
- Addition Rule of Integration
- Subtraction Rule of Integration
- Constant Multiple Rule of Integration
- Antiderivative: Integration as Inverse Process of Differentiation
- Integration Formulas
- Types of Integration
- Definite Integration
- Indefinite Integration
- Improper Integration
- Integration Techniques
- Integration of Basic Functions
- Integration of Constant Function
- Integration of Trigonometric Functions
- Integration of Exponential and Logarithmic Functions
- Applications of Integration
- Integration in Physics and Engineering
- Integration in Economics and Finance
- Integration vs Differentiation
- Solved Examples on Integration
- Practice Questions on Integration
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