9 Techniques of Integration
Most of us find integration difficult – basically because we are always trying to ‘undo’
some differentiation, which might have been difficult in the first place! There are no short
cuts to good integration skills – practice, practice, practice is the only way. Plenty of that
is provided in this chapter. In this case the review test covers a wide range, which reflects
the importance of the material.
Prerequisites
It will be helpful if you know something about:- differentiation (Chapter 8
➤
)- properties of the elementary functions (Chapters 4, 6)
- partial fractions (62
➤
)- completing the square (66
➤
)Objectives
In this chapter you will find:- definition of integration
- standard integrals
- addition of integrals
- simplifying the integrand
- linear substitution in integration
- thedu=f′(x)dxsubstitution
- integration of rational functions
- use of trig identities in integration
- using trig substitutions in integration
- integration by parts
- choice of integration methods
- definite integrals
Motivation
You may need the material of this chapter for:- solving differential equations (➤Chapter 15)
- calculating areas and volumes (➤Chapter 10)
- calculating mean and RMS values (➤Chapter 10)
- calculating moments, centroids, etc. (➤Chapter 10)
- calculating means, standard deviations, and probabilities