__BASIC CONCEPT__

__BASIC CONCEPT__**Let F(x) be a differentiable function of x such that**

**Then F(x) is called the integral of f(x).**

**Symbolically, it is written as **

**f(x) , the function to be integrated , is called the integrand.**

**F(x) is also called the anti-derivative (or primitive function) of f(x).**

__Constant of Integration:__

__Constant of Integration:__**As the differential coefficient of a constant is zero, we have**

**Therefore, **

**This constant c is called the constant of integration and can take any real value**

__Properties of Indefinite Integration:__

__Properties of Indefinite Integration:__**(i) ( Here ‘ a ‘ is a constant)**

**(ii) **

**(iii) If **

**Then **

__Integration as the Inverse Process of Differentiation :__

**Evaluate :**

**(i) **

**(ii) **

**(iii) **

**(iv) **

**Solutions: (i) **

**= tanx – x + c**

**(ii) **

**Here e ^{x}(cosx − sinx) is the derivative of e^{x} cosx.**

**=> I = e ^{x}cosx + c.**

**(iii) **

**Here 3x ^{1/2}(1 + x^{3/2}) is the derivative of (1 + x^{3/2})^{2}**

**=> I = (1 + x ^{3/2})^{2} + c.**

**(iv) **

**NOTE : When solving such problems it is expedient to use the following trigonometric identities :**

**Here **

**=> **

**Exercise :**

**Integrate the following functions**

**(i) **

**(ii) **

**(iii) **

**(iv) **

**Basic formulae :**

**Basic formulae :**

__Standard Formulae:__

__Standard Formulae:__