Rules for Integration
Some important rules of integration are:
- Power Rule
- Addition Rule
- Subtraction Rule
- Constant Multiple Rule
Power Rule of Integration
The Power Rule of Integration is a fundamental rule for finding the antiderivative (indefinite integral) of a function in the form of a power of x, The power rule of integration is stated as:
∫xn dx = xn+1/ (n + 1)
Addition Rule of Integration
The Addition Rule of Integration allows you to integrate the sum of two functions by integrating each function separately and then adding the results. The addition rule of integration is stated as:
∫{f(x) + g(x)} dx = ∫f(x) dx + ∫g(x) dx
Subtraction Rule of Integration
The Subtraction Rule of Integration is similar to the Addition Rule of Integration. It allows you to integrate the difference of two functions by integrating each function separately and then subtracting the results. The subtraction rule of integration is stated as:
∫{f(x) – g(x)} dx = ∫f(x) dx – ∫g(x) dx
Constant Multiple Rule of Integration
The Constant Multiple Rule of Integration states that if you have a constant multiplied by a function, you can factor out the constant and then integrate the function The multiplication of constant rule of integration can be stated as:
∫k f(x) dx = k ∫f(x) dx,
Where k is constant.
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