Lab6B_Ex4 - Exercise 4 1 f 5 Cos 2 2 Cos Cos Cos,5 2 5 2...

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Exercise4 H 1 L f @ Θ_ , Φ_ D = 8H 2 + Cos @ Φ DL Cos @ Θ D + 5, H 2 + Cos @ Φ DL Sin @ Θ D + 5, Sin @ Φ D + 5 < 8 5 + Cos @ Θ D H 2 + Cos @ Φ DL , 5 + H 2 + Cos @ Φ DL Sin @ Θ D , 5 + Sin @ Φ D< ABDSD = ParametricPlot3D @ f @ Θ , Φ D , 8 Θ , 0, 2 Π < , 8 Φ , 0, 2 Π <D 2 4 6 8 x 2 4 6 8 y 4.0 4.5 5.0 5.5 6.0 z H 2 L
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B @ x _ , y _ , z _ D = 8 - y, x, - 5 z 6 < BDS = VectorFieldPlot3D @ B @ x, y, z D , 8 x, 2, 8 < , 8 y, 2, 8 < , 8 z, 4, 6 <D Show @ ABDSD, BDS, PlotRange fi 88 2, 8 < , 8 2, 8 < , 8 4, 6 <<D : - y, x, - 5z 6 > 2 4 6 8 x 2 4 6 8 y 4.0 4.5 5.0 5.5 6.0 z 2 4 6 8 x 2 4 6 8 y 4.0 4.5 5.0 5.5 6.0 z integrand = Apply @ B, f @ Θ , Φ DD .Cross @ D @ f @ Θ , Φ D , Θ D , D @ f @ Θ , Φ D , Φ DD Integrate @ integrand, 8 Θ , 0, 2 Π < , 8 Φ , 0, 2 Π <D H 5 + Cos @ Θ D H 2 + Cos @ Φ DLL I 2Cos @ Φ D Sin @ Θ D + Cos @ Φ D 2 Sin @ Θ DM + I 2Cos @ Θ D Cos @ Φ D + Cos @ Θ D Cos
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