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CHAPTER 8 : APPLICATIONS OF THE DEFINITE INTEGRALS

8.1 Introduction

In this chapter we shall learn how to apply the technique of the Definite Integral to obtain areas, volumes, mean values, work done, fluid pressure etc.

For the evaluation of areas and volumes it is necessary to know the nature of the curve. Hence we shall study below the shapes of certain well-known curves.

(1) Straight Line :

The general for + m : ax + by c = 0

(2) Circle :       

(3) (a) Standard Parabola : The general equations of the parabolas are

Y2 = 4 ax,   y2 = - 4 ax,   x2 = 4 by    and    x2 = -4 by

                                

                                

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Index

8.1 Introduction
8.2 Area
8.3 Volumes
8.4 Mean Value
8.5 Arc Length(Rectification)

Chapter 1

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