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Note :

i) The word integration literally means to add together small bits. Now the question arises that is there any connection between the two meanings of integration :

(i) The Inverse of differentiation.

(ii) The Adding together of small bits.

Yes, there is such a connection between the above said two concepts. This, has been mentioned later in the fundamental theorem of Integral calculus.

ii) Also note that the constant " c " in the above discussion is known as the constant of integration.

iii) Any integral of f ( x ) is in the form f ( x ) + c. which is known as the general integral of f ( x ).

An integral obtained by giving particular value to ‘ c ’ is called a particular integral.

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Some Standard Results

Given below are some standard results, obtained by using the derivatives of some well-known functions.

(1)

(2)

(3)

(4)

(5)

(For the sake of convenience it is customary to omit the modulus sign)

Index

6.1 Anti-derivatives (indefinite Integral)
6.2 Integration Of Some Trignometric Functions
6.3 Methods Of Integration
6.4 Substitution And Change Of Variables
6.5 Some Standard Substitutions
6.6 Integration By Parts
6.7 Integration By Partial Fractions

Chapter 7