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Unformatted text preview: February 2, 2005
Announcements T. Toro's office hours have been cancelled today. Today 7.2 Trigonometric Integrals 1 Trigonometric identities sin2 x + cos2 x = 1 sin2 x = 1 (1  cos 2x) 2 2 x = 1 (1 + cos 2x) cos 2 sin x cos x = 1 sin 2x 2 1 sin a cos b = [sin(a  b) + sin(a + b)] 2 sin a sin b = 1 [cos(a  b)  cos(a + b)] 2 1 cos a cos b = [cos(a  b) + cos(a + b)] 2 Strategy for evaluating
1. If n = 2k + 1 then sinm x cos2k+1 x dx = = sinm x cosn x dx sinm x(cos2 x)k cos x dx sinm x(1  sin2 x)k cos x dx Then substitute u = sin x and integrate um (1  u2 )k du. 2. If m = 2k + 1 then sin2k+1 x cosn x dx = = (sin2 x)k cosn x sin x dx (1  cos2 x)k cosn x sin x dx Then substitute u = cos x and integrate  un(1  u2 )k du. 3. If m = 2k and n = 2j then sin
2k x cos 2j x dx = 1  cos 2x 2 k 1 + cos 2x 2 j dx ...
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This note was uploaded on 03/09/2008 for the course CALC 1,2,3 taught by Professor Varies during the Spring '08 term at Lehigh University .
 Spring '08
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 Calculus, Integrals

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