notes 2 - Math 1432 Notes Session 2 Notes Section 8.3...

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Math 1432 Notes – Session 2 Notes Section 8.3 Calculating Integrals involving powers of Trig functions xdx x n m cos sin If m or n odd: a. m odd: rewrite x m sin as x x m sin sin 1 - ( m -1 is even so can use identity x x 2 2 cos 1 sin - = ) b. n odd: rewrite x m cos as x x m cos cos 1 - ( n -1 is even so can use identity x x 2 2 sin 1 cos - = ) If m and n even use these identities: x x x x x x x 2 cos 2 1 2 1 cos 2 cos 2 1 2 1 sin 2 sin 2 1 cos sin 2 2 + = - = = example: 3 2 sin cos x xdx
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If you are given one of these where n m ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 dx nx mx dx nx mx dx nx mx cos cos sin sin cos sin Use these formulas: ( 29 ( 29 [ ] ( 29 ( 29 [ ] ( 29 ( 29 [ ] B A B A B A B A B A B A B A B A B A + + - = + - - = + + - = cos cos 2 1 cos cos cos cos 2 1 sin sin sin sin 2 1 cos sin example: dx x x ) 3 sin( ) 2 cos(
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For dx x x n m sec tan a. n even: rewrite x x n m sec tan as x x x n m 2 2 sec sec tan - (then you can use identity 1 tan sec 2 2 + = x x ) b. m odd: rewrite
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This note was uploaded on 03/07/2012 for the course MATH 11278 taught by Professor Jeffmorgan during the Summer '10 term at University of Houston.

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notes 2 - Math 1432 Notes Session 2 Notes Section 8.3...

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