## mahmit2012 3 years ago LEC3:Quintet Integrals and Three Technic-2.

1. experimentX

well ... the original question is http://math.stackexchange.com/questions/172089/use-stokess-theorem-to-show-oint-c-y-dx-z-dy-x-dz-sqrt3-pi-a2 but i would also be interested in knowing how to write circles and hemispheres ... that is slant.

2. experimentX

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4. experimentX

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10. experimentX

for a slant circle it got ParametricPlot3D[{1/Sqrt[6] (Sqrt[3] Cos[t] + Sin[t]), 1/Sqrt[6] (-Sqrt[3] Cos[t] + Sin[t]), 2/Sqrt[6] Sin[t]}, {t, 0, 2 Pi}] and for slant circular surface i got ParametricPlot3D[{ u 1/Sqrt[6] (Sqrt[3] Cos[t] + Sin[t]), u 1/Sqrt[6] (-Sqrt[3] Cos[t] + Sin[t]), u 2/Sqrt[6] Sin[t]}, {u, 0, 1}, {t, 0 , 2 Pi}] could you verify it http://www.wolframalpha.com/input/?i=ParametricPlot3D [{+u+1%2FSqrt[6]+%28Sqrt[3]+Cos[t]+%2B++Sin[t]%29%2C++++u+1%2FSqrt[6]+%28-Sqrt[3]+Cos[t]+%2B++Sin[t]%29%2C++u+2%2FSqrt[6]++Sin[t]}%2C+{u%2C++++0%2C+1}%2C+{t%2C+0+%2C+2+Pi}] still i'm not getting parametric surface for slant hemisphere.