PROGRAMME 15 INTEGRATION 1.

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PROGRAMME 15 INTEGRATION 1

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

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

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

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

Programme 15: Integration 1 Introduction Standard integrals

Programme 15: Integration 1 Introduction Standard integrals

Programme 15: Integration 1 Introduction Standard integrals

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

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

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 Integrals of the form and (a) For example: (b)

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

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

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

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:

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

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

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