Lesson 7b Wallis Formula

Lesson 7b Wallis - 29 29 29 29 29 2 5 1 1 2 4 6 8 10 2 4 6 2 8 dx x sin x cos 8 2 3 2 7 = = • = 29 29 29 29 29 29 29 29 143 768 35 2 2 4 6 8 1

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Click to edit Master subtitle style 8/19/11 WALLI’S FORMULA
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Click to edit Master subtitle style 8/19/11 TRIGONOMETRIC TRANSFORMATION WALLI’S FORMULA OBJECTIVES: recall and apply the different trigonometric identities in transforming powers of sine and cosine; and use Walli’s Formula to shorten the solution in finding the antiderivative of powers of sine and cosine
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Click to edit Master subtitle style 8/19/11 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 = = - + - + + - - - - = 1 otherwise even are n and m when 2 where ......... 4 n m 2 n m n m 3 n 1 n ...... 3 m 1 m d cos sin sFormula ' Walli 2 0 n m α π θ
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Click to edit Master subtitle style 8/19/11 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 12885 . 0 512 21 2 2 4 6 8 10 1 3 5 7 1 3 dx x sin x cos 3 . 1 2 2 0 8 = = = π ( 29 ( 29 ( 29 ( 29
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Unformatted text preview: ( 29 ( 29 ( 29 ( 29 ( 29 2 . 5 1 1 2 4 6 8 10 2 4 6 2 8 dx x sin x cos 8 . 2 3 2 7 = = • = ∫ ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 143 . 768 35 2 2 4 6 8 1 3 5 7 3 1 x 3 cos . 3 6 8 = = • • = ∫ 2 6 3 u ; 6 x when u ; x when dx 3 du ; x 3 letu = = = = = = = EXAMPLE Evaluate the following integrals. Click to edit Master subtitle style 8/19/11 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 229 . 1 1 3 5 7 2 4 6 2 1 x 2 sin . 4 4 7 = • • = ∫ π 2 4 2 u ; 4 x when u ; x when dx 2 du ; x 2 letu = = = = = = =...
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This note was uploaded on 08/19/2011 for the course ECON 232 taught by Professor Charles during the Spring '11 term at MIT.

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Lesson 7b Wallis - 29 29 29 29 29 2 5 1 1 2 4 6 8 10 2 4 6 2 8 dx x sin x cos 8 2 3 2 7 = = • = 29 29 29 29 29 29 29 29 143 768 35 2 2 4 6 8 1

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