Antiderivative: Integration as Inverse Process of Differentiation
The process of finding the antiderivative i.e., the inverse of the derivative is called integration. If Φ(x) is a function and the derivative of Φ(x) is f(x) then, integration of f(x) results in Φ(x).
(d / dx) {Φ(x)} = f(x) ⇔ ∫f(x) dx = Φ(x) + C
OR
∫[d/dx]g(x) dx = g(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