Programme 18 Reduction formulas PROGRAMME 18 REDUCTION FORMULAS

Programme 18: Reduction formulas PROGRAMME 18 REDUCTION FORMULAS STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Definite integrals Integrands of the form STROUD and Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Definite integrals Integrands of the form STROUD and Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Using the integration by parts formula: it is easily shown that: STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Writing: then can be written as: This is an example of a reduction formula. STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Sometimes integration by parts has to be repeated to obtain the reduction formula. For example: STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Definite integrals Integrands of the form STROUD and Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Definite integrals Integrands of the form STROUD and Worked examples and exercises are in the text

Programme 18: Reduction formulas Definite integrals When the integral has limits the reduction formula may be simpler. For example: STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Definite integrals Integrands of the form STROUD and Worked examples and exercises are in the text

Programme 18: Reduction formulas Generating a reduction formula Definite integrals Integrands of the form STROUD and Worked examples and exercises are in the text

Programme 18: Reduction formulas Integrands of the form The reduction formula for and is and. . . STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Integrands of the form the reduction formula for and is: These take interesting forms when evaluated as definite integrals between 0 and π/2 STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Integrands of the form The reduction formulas for and are both: where (a) If n is even, the formula eventually reduces to I 0 = π/2 (b) If n is odd the formula eventually reduces to I 1 = 1 STROUD Worked examples and exercises are in the text

Programme 18: Reduction formulas Learning outcomes üIntegrate by parts and generate a reduction formula üIntegrate by parts using a reduction formula üEvaluate integrals with integrands of the form sinnx and cosnx using reduction formulas STROUD Worked examples and exercises are in the text