PROGRAMME 16 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
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
Introduction Integration is the reverse process of differentiation. For example: where C is called the constant of integration.
Introduction Standard integrals What follows is a list of basic derivatives and associated basic integrals:
Introduction Standard integrals
Introduction Standard integrals
Introduction Standard integrals
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
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
Functions of a linear function of x If: then: For example:
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
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
Integrals of the form and For example: (b)
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
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
Integration of products – integration by parts The parts formula is: For example:
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
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
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:
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
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
Integration of trigonometric functions Many integrals with trigonometric integrands can be evaluated after applying trigonometric identities. For example:
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