Integration of Basic Functions
There are different integration formulas for different functions. Below we will discuss the integration of different functions in depth and get complete knowledge about the integration formulas.
Integration of Constant Function
The integration of a constant function is given by:
∫k dx = kx + C, where k is constant
Integration of Trigonometric Functions
The integration of trigonometric functions is given by:
- ∫sin x dx = -cos x + C
- ∫cos x dx = sin x + C
- ∫sec2x dx = tan x + C
- ∫cosec2x dx = -cot x + C
- ∫sec x tan x dx = sec x + C
- ∫cosec x cot x dx = – cosec x + C
- ∫tan x dx = -log |cos x| + C
- ∫cot x dx = log |sin x| + C
- ∫sec x dx = log |sec x + tan x| + C
- ∫cosec x dx = log |cosec x – cot x| + C
Integration of Exponential and Logarithmic Functions
The integration of exponential and logarithmic function is given by:
- ∫(1 / x) dx = loge|x| + C
- ∫ex dx = ex + C
- ∫ax dx = [ax/ logea] + C
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