# Integration Rules and Integration definition with examples

## Integration Rules and Integration Definition with Concepts, Formulas, Examples and Worksheets.ย

## A Complete Preparation Book for Integration (Calculus)ย

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**Basic examples of Integration rulesย**

**Ifย ย ย y = 2x + 7ย**

**orย ย y = 2x – 8**

**orย ย y = 2x + 100000**

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**then for all casesย dy/dx = 2**

**Hence we can say that anti-derivative orย **

**integral of 2 is 2x + C**

**where C = any real constant.ย **

**Can you guess what is the integration of 2x ? well to learn Integration completely you can download my free eBook named Indefinite and Definite Integration Rules and Theory with Examples and Exerciseย **

**Q: What are the Integrate Synonym?**

**Ans: Integrate Synonym or another word for Integrate are Integral or Integration or primitive or an anti-derivative of a function.**

## Integration Definition

## Basic Integration Rules using integration definition

## Comparison between Differentiation and Integration.

## CONTENTS OF INTEGRATION RULES AND DEFINITION WITH EXAMPLES COMPLETE THEORY AND EXERCISE.ย ย

## DOWNLOAD INTEGRATION E-BOOK FOR FREE

Comparison between Differentiation and Integration

Integration Rules

Properties of Integration

Methods to find Integral

Fundamental Integration Rules

Integration Rules by Substitution

Integration Rules by Parts formula

Integral Calculus formulas

Evaluation of the various forms of Integrals by use of Standard results

Integration Rules of different standard formsย

Integration Rules of rational functions by using Partial fractions

Integration Rules of Trigonometric functions

Integration Rules of Quadratic functionsย

Integration Rules using Euler’s substitution

Some integrals which can not be found.

Definite Integral as the Limit of a Sum Rulesย

Definite Integration by Substitution Rules

Properties of Definite Integration

Summation of Series by Integration Rules

Solving Integral Equations

Derivatives of Integrals Rules

Gamma Function Rules

Reduction formula for Definite Integration Rules

Walli’s Formula for Integration Rules

Leibnitz’s Integration Rules

Integration Rules with Infinite Limits(Improper Integrals)

Some important Definite Integration Rules

Integration Rules of Piece-wise Continuous Function

Integral Calculus Examples

**HISTORY OF INTEGRATION**

**The origin of the integration goes back to the early period of development of mathematics and it is related to the method of exhaustion developed by the mathematicians of ancient Greece. This method arose in the solution of problems on calculating areas and volumes of solid bodies etc. In this sense, the method of exhaustion can be regarded as an early method of Integration.**

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**The greatest development in integration is method of exhaustion in the early period was obtained in the works of Eudoxus (440 B.C.) and Archimedes (300 B.C.) Conclusively, the fundamental concepts and theory and integration and primarily its relationship with differential calculus were developed in the work of P.de Fermat, I. Newton and G.Leibnitz at the end of 17th century A.D.**

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**Newton introduced the basic notion of inverse function called the anti-derivative (Integration) or the inverse method of tangents.**

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**During 1684-86 A.D. Leibnitz published an article in the Acta Eruditorum which he called Calculas summatorius, since it was connected with the summation of a number of infinitely small areas, whose sum, he indicated by the symbol โซ. In 1696 A.D. he followed a suggestion made by J.Bernoulli and changed this article to calculus integrali. This corresponded to Newton’s inverse method of tangents.ย**

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**Both Newton and Leibnitz adopted quite independent lines of approach which were radically different. However, respective theories accomplished results that were practically identical. Leibnitz used the notion of definite integration and what is quite certain is that he first clearly appreciated tie up between the anti-derivative and the definite integral. The discovery that differentiation and integration are inverse operations belongs to Newton and Leibnitz.**

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