1. PROGRAMME 16
INTEGRATION 1

2. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

3. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

4. Introduction
Integration is the reverse process of differentiation. For example:
where C is called the constant of integration.

5. Introduction
Standard integrals
What follows is a list of basic derivatives and associated basic integrals:

6. Introduction
Standard integrals

7. Introduction
Standard integrals

8. Introduction
Standard integrals

9. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

10. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

11. Functions of a linear function of x
If:
then:
For example:

12. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

13. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

14. Integrals of the form and
For example:
(b)

15. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

16. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

17. Integration of products – integration by parts
The parts formula is:
For example:

18. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

19. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

20. Integration by partial fractions
If the integrand is an algebraic fraction that can be separated into its partial fractions then each individual partial fraction can be integrated separately.
For example:

21. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

22. Introduction
Functions of a linear function of x
Integrals of the form and
Integration of products – integration by parts
Integration by partial fractions
Integration of trigonometric functions

23. Integration of trigonometric functions
Many integrals with trigonometric integrands can be evaluated after applying trigonometric identities.
For example:

24. Learning outcomes
Integrate standard expressions using a table of standard forms
Integrate functions of a linear form
Evaluate integrals with integrands of the form and
Integrate by parts
Integrate by partial fractions
Integrate trigonometric functions