Section 14.7 - y x x y x ---+ 2 4 16 2 2 2 2 2 Triple...

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Section 14.7 Triple Integrals in Cylindrical and Spherical Coordinates
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In general, to convert from rectangular triple integrals to cylindrical ∫ ∫ ∫ ∫ ∫ ∫ = Q g g r r h r r h rdzdrd z r r f dV z y x f 2 1 2 1 2 1 ) ( ) ( ) sin , cos ( ) sin , cos ( ) , sin , cos ( ) , , ( θ
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To visualize a particular order of integration, view the inetgral in terms of sweeping motions.
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Example Convert the integral from rectangular to cylindrical coordinates. dzdydx y x x y x ∫ ∫ - - - + 2 0 4 0 16 0 2 2 2 2 2
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Example Convert the integral from rectangular to spherical coordinates. dzdydx
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Unformatted text preview: y x x y x ---+ 2 4 16 2 2 2 2 2 Triple integrals involving spheres or cones are often easier to evaluate in spherical coordinates d d d f dV z y x f Q sin ) cos , sin sin , cos sin ( ) , , ( 2 2 1 2 1 2 1 = Once again, visualize the order of integration in terms of sweeping motions Figure 14.68...
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Section 14.7 - y x x y x ---+ 2 4 16 2 2 2 2 2 Triple...

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