1. PROGRAMME 15
INTEGRATION 1

2. Programme 15: Integration 1
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
Programme 15: Integration 1

3. Programme 15: Integration 1
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
Programme 15: Integration 1

4. Programme 15: Integration 1
Introduction
Integration is the reverse process of differentiation. For example:
where C is called the constant of integration.

5. Programme 15: Integration 1
Introduction
Standard integrals
What follows is a list of basic derivatives and associated basic integrals:

6. Programme 15: Integration 1
Introduction
Standard integrals

7. Programme 15: Integration 1
Introduction
Standard integrals

8. Programme 15: Integration 1
Introduction
Standard integrals

9. Programme 15: Integration 1
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
Programme 15: Integration 1

10. Programme 15: Integration 1
Functions of a linear function of x
If:
then:
For example:

11. Programme 15: Integration 1
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

12. Programme 15: Integration 1
Integrals of the form and
(a)
For example:
(b)

13. Programme 15: Integration 1
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
Programme 15: Integration 1

14. Programme 15: Integration 1
Integration of products – integration by parts
The parts formula is:
For example:

15. Programme 15: Integration 1
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
Programme 15: Integration 1

16. Programme 15: Integration 1
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:

17. Programme 15: Integration 1
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
Programme 15: Integration 1

18. Programme 15: Integration 1
Integration of trigonometric functions
Many integrals with trigonometric integrands can be evaluated after applying trigonometric identities.
For example:

19. Programme 15: Integration 1
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