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INDEFENITE INTEGRAL

Introduction of Indefinite Integral

• Introduction
• Definition
• Integration as inverse process of differentiation
• Anti derivatives of some special function
• Integral of Algebraic, Exponential, Exponent, square root and reciprocal function
• Assignment

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Outline

INDFINITE INTEGRAL

∫

∫

∫

∫

∫

∫

∫

∫

∫

A

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- -- - - - - - - - - - - - - - - - - - - - - - -

B

x

t=0 hrs

t=t hrs.

Unknown displacement

INTRODUCING THE CONCEPT OF INDEFINITE INTEGRAL

Velocity of a moving car is rate of change of displacement

v (t) = x(t) km/h

Then unknown displacement can be obtain as

INTRODUCTION �

If a function f is differentiable in an interval I

i.e. its derivative f' exists at each point of I,

then the function that could possibly have given function as a derivative,is called anti derivatives (or primitives) of the function.

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ANTI DERIVATIVE OF A FUNCTION

Definition

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• The function f(x) is called an anti derivative of F(x)

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• if f '( x) = F(x) and is written as

f(x) = ∫ F(x) dx

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INTEGRATION AS AN INVERSE PROCESS OF DIFFERENTIATION

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where C is called the constant of integration

Similarly we can obtain

5.

=>

6.

=>

2)

3)

Anti derivative of some more function

INTEGRALS OF SOME SPECIAL FUNCTIONS