Chapter6_12 - − − = − − = − = − = = ...

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PHY3063 R. D. Field Department of Physics Chapter6_12.doc University of Florida Useful Math Trigonometric Relations: ) sin( ) sin( cos sin 2 ) cos( ) cos( sin sin 2 ) cos( ) cos( cos cos 2 sin sin cos cos ) cos( sin cos cos sin ) sin( B A B A B A B A B A B A B A B A B A B A B A B A B A B A B A + + = + = + + = = ± ± = ± m Indefinite Integrals: 4 2 cos 2 sin 8 1 4 6 cos 8 2 cos 4 2 sin 4 cos 4 2 sin 2 cos sin cos cos 4 2 cos 2 sin 8 1 4 6 sin 8 2 cos 4 2 sin 4 sin 4 2 sin 2 sin cos sin sin 2 sin cos sin 2 3 2 2 2 2 2 2 3 2 2 2 2 2 2 x x x x x xdx x x x x x xdx x x x xdx x x x xdx x x x x x x xdx x x x x x xdx x x x xdx x x x xdx x x xdx x + + = + + = + = + =
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Unformatted text preview: − − = − − = − = − = = ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ Definite Integrals: ) ( 2 sin 2 cos cos 2 sin sin 1 2 2 n dx e x dx x x nxdx mx nxdx mx x n mn mn Γ = = = = ∫ ∫ ∫ ∫ ∞ − − ∞ π δ ) ( ) 1 ( n n n Γ = + Γ = Γ ) ( 2 1...
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