PROGRAMME 15 INTEGRATION 1 STROUD Worked examples and

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PROGRAMME 15 INTEGRATION 1 STROUD Worked examples and exercises are in the text

PROGRAMME 15 INTEGRATION 1 STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Functions of a linear function of x Integrals of

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 STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Functions of a linear function of x Integrals of

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 STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Integration is the reverse process of differentiation. For example:

Programme 15: Integration 1 Introduction Integration is the reverse process of differentiation. For example: where C is called the constant of integration. STROUD Worked examples and exercises are in the text

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

Programme 15: Integration 1 Introduction Standard integrals What follows is a list of basic derivatives and associated basic integrals: STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Standard integrals STROUD Worked examples and exercises are in

Programme 15: Integration 1 Introduction Standard integrals STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Standard integrals STROUD Worked examples and exercises are in

Programme 15: Integration 1 Introduction Standard integrals STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Standard integrals STROUD Worked examples and exercises are in

Programme 15: Integration 1 Introduction Standard integrals STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Functions of a linear function of x Integrals of

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 STROUD Worked examples and exercises are in the text

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

Programme 15: Integration 1 Functions of a linear function of x If: then: For example: STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Functions of a linear function of x Integrals of

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 STROUD Worked examples and exercises are in the text

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

Programme 15: Integration 1 Integrals of the form and (a) For example: (b) For example: STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Functions of a linear function of x Integrals of

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 STROUD Worked examples and exercises are in the text

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

Programme 15: Integration 1 Integration of products – integration by parts The parts formula is: For example: STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Functions of a linear function of x Integrals of

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 STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Integration by partial fractions If the integrand is an algebraic

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: STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Introduction Functions of a linear function of x Integrals of

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 STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Integration of trigonometric functions Many integrals with trigonometric integrands can

Programme 15: Integration 1 Integration of trigonometric functions Many integrals with trigonometric integrands can be evaluated after applying trigonometric identities. For example: STROUD Worked examples and exercises are in the text

Programme 15: Integration 1 Learning outcomes üIntegrate standard expressions using a table of standard

Programme 15: Integration 1 Learning outcomes üIntegrate standard expressions using a table of standard forms üIntegrate functions of a linear form üEvaluate integrals with integrands of the form and üIntegrate by parts üIntegrate by partial fractions üIntegrate trigonometric functions STROUD Worked examples and exercises are in the text

PROGRAMME 18 INTEGRATION APPLICATIONS 1 STROUD Worked examplesPROGRAMME 18 INTEGRATION APPLICATIONS 1 STROUD Worked examples
PROGRAMME 14 SERIES 2 STROUD Worked examples andPROGRAMME 14 SERIES 2 STROUD Worked examples and
PROGRAMME F 10 FUNCTIONS STROUD Worked examples andPROGRAMME F 10 FUNCTIONS STROUD Worked examples and
PROGRAMME 27 STATISTICS STROUD Worked examples and exercisesPROGRAMME 27 STATISTICS STROUD Worked examples and exercises
PROGRAMME 3 HYPERBOLIC FUNCTIONS STROUD Worked examples andPROGRAMME 3 HYPERBOLIC FUNCTIONS STROUD Worked examples and
PROGRAMME F 8 TRIGONOMETRY STROUD Worked examples andPROGRAMME F 8 TRIGONOMETRY STROUD Worked examples and
PROGRAMME 27 STATISTICS STROUD Worked examples and exercisesPROGRAMME 27 STATISTICS STROUD Worked examples and exercises
PROGRAMME F 10 FUNCTIONS STROUD Worked examples andPROGRAMME F 10 FUNCTIONS STROUD Worked examples and
PROGRAMME F 11 DIFFERENTIATION STROUD Worked examples andPROGRAMME F 11 DIFFERENTIATION STROUD Worked examples and
PROGRAMME 23 MULTIPLE INTEGRALS STROUD Worked examples andPROGRAMME 23 MULTIPLE INTEGRALS STROUD Worked examples and
PROGRAMME 13 SERIES 1 STROUD Worked examples andPROGRAMME 13 SERIES 1 STROUD Worked examples and
PROGRAMME 8 DIFFERENTIATION APPLICATIONS STROUD Worked examples andPROGRAMME 8 DIFFERENTIATION APPLICATIONS STROUD Worked examples and
PROGRAMME F 4 GRAPHS STROUD Worked examples andPROGRAMME F 4 GRAPHS STROUD Worked examples and
PROGRAMME 1 COMPLEX NUMBERS 1 STROUD Worked examplesPROGRAMME 1 COMPLEX NUMBERS 1 STROUD Worked examples
PROGRAMME 8 DIFFERENTIATION APPLICATIONS 1 STROUD Worked examplesPROGRAMME 8 DIFFERENTIATION APPLICATIONS 1 STROUD Worked examples
PROGRAMME F 7 PARTIAL FRACTIONS STROUD Worked examplesPROGRAMME F 7 PARTIAL FRACTIONS STROUD Worked examples
Programme 5 Matrices PROGRAMME 5 MATRICES STROUD WorkedProgramme 5 Matrices PROGRAMME 5 MATRICES STROUD Worked
Programme 7 Differentiation PROGRAMME 7 DIFFERENTIATION STROUD WorkedProgramme 7 Differentiation PROGRAMME 7 DIFFERENTIATION STROUD Worked