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Review of Trigonometric Integrals

Review of Trigonometric Integrals - Review Trigonometric...

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Review Trigonometric Integrals
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I. ∫cos n x dx Case 1 : n is an odd natural number c x x dx x x x dx x x dx x x dx x c x dx x + - = - = - = = + = 3 sin sin ) cos sin (cos cos ) sin 1 ( cos cos cos . 2 sin cos . 1 3 2 2 2 3
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c x x dx x x x dx x x x dx x x x dx x x c x dx x x + - = - = - = = + = 23 sin 21 sin cos ) sin (sin cos ) sin 1 ( sin cos cos sin cos sin . * 2 21 sin cos sin . * 1 23 21 22 20 2 20 2 20 3 20 21 20
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c x x dx x x x dx x x x dx x x x dx x x + - = - = - = = - - - 3 7 sin 3 1 sin cos ) sin (sin cos ) sin 1 ( sin cos cos sin sin cos *. * 2 3 7 3 1 3 4 3 2 2 3 2 2 3 2 3 2 3
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c x x x dx x x x dx x x dx x x dx x + + - = + - = - = = 5 sin 3 sin 2 sin cos ) sin sin 2 1 ( cos ) sin 1 ( cos cos cos . 3 5 3 4 2 2 2 4 5
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c x x x x c x x x x dx x x x x dx x x dx x x dx x + - + - = + - + - = - + - = - = = 7 sin 5 sin 3 sin sin 7 sin 5 sin 3 3 sin 3 sin cos ) sin sin 3 sin 3 1 ( cos ) sin 1 ( cos cos cos . 4 7 5 3 7 5 3 6 4 2 3 2 6 7
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I. ∫cos n x dx Case 2 : n is an even natural number [ ] c x x dx x x dx x dx dx x dx x + + = + = + = + = 2 sin 4 1 2 1 2 2 cos 2 1 2 1 2 1 2 cos 2 1 2 2 cos 1 cos . 1 2
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