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PROGRAMME 16 INTEGRATION 1
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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
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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
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Introduction Integration is the reverse process of differentiation. For example: where C is called the constant of integration.
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Introduction Standard integrals What follows is a list of basic derivatives and associated basic integrals:
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Introduction Standard integrals
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Introduction Standard integrals
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Introduction Standard integrals
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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
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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
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Functions of a linear function of x
If: then: For example:
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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
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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
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Integrals of the form and
For example: (b)
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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
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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
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Integration of products – integration by parts
The parts formula is: For example:
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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
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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
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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:
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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
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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
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Integration of trigonometric functions
Many integrals with trigonometric integrands can be evaluated after applying trigonometric identities. For example:
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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
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