Integration
What does Integration mean?
The process of finding the anti-derivative of the function is called the integration.
What is an Integral in Math?
An integral in math is a concept used to find the area under a curve or the sum of quantities over an interval.
What is the Notation of Integration?
The notation of the integration is ∫.
What is the Fundamental Theorem of Calculus?
The Fundamental Theorem of Calculus states that the integral of a function’s derivative over an interval is equal to the difference in the function’s values at the interval’s endpoints.
How to Evaluate Integration of Function?
To evaluate the integration of a function, we can use integration formulas, Integration by substitution, Integration by parts, and Integration by partial fraction.
What is the Difference Between Definite and Indefinite Integrals?
A definite integral computes the exact numerical value of the quantity between specified limits, whereas an indefinite integral, represents a family of functions related to the original function without specific limits.
What are Some Applications of Integration in Real Life?
Some applications of integration are finding area of the curve, finding the area between two curves and volumes etc.
What is Integral and Its Types?
Integral is also known as continuous summation as it is defined as the limit of discrete summation when the limit of parameter approaches infinite. There are three types of integrals: Indefinite, Definite and Improper Integral.
What are Improper Integrals?
Improper integrals are integrals where one or both of the integration limits are infinite, or the integrand has a singularity within the interval.
What are the Different Methods to find Integration?
The different methods to find integration are:
- Integration by Substitution
- Integration by Parts
- Integration by Partial Fraction
What is Integration by Substitution?
Integration by substitution is a method in calculus to simplify the integration of complex functions by replacing variables with new ones, making the integral easy to calculate.
What is Integration by Parts?
Integration by parts is a technique in calculus for finding the integral of a product of two functions. It involves using a formula derived from the product rule for differentiation.
What is Integration by Partial Fraction?
Integration by partial fractions is a technique in calculus used to decompose a rational function into simpler fractions, making it easier to integrate each term separately.
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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