- #1

imana41

- 36

- 0

this Q want to check Stokes' theorem ? for [URL]http://latex.codecogs.com/gif.latex?F=(x^2,xy,-z^2)[/URL] and surface [URL]http://latex.codecogs.com/gif.latex?x^2+y^2+z^2=1[/URL] and [URL]http://latex.codecogs.com/gif.latex?z\geqslant%200[/URL]

i should equal [PLAIN]http://latex.codecogs.com/gif.latex?\oint%20Mdx+ndy+pdz

with [PLAIN]http://latex.codecogs.com/gif.latex?\int%20\int%20curlF.n.d\sigma

i know : curlF=(0,0,y) and n=(x,y,z) and [URL]http://latex.codecogs.com/gif.latex?d\sigma%20=\frac{dxdy}{z}[/URL] and [PLAIN]http://latex.codecogs.com/gif.latex?\int%20\int%20curlF.n.d\sigma = [URL]http://latex.codecogs.com/gif.latex?\int_{-1}^{1}\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}ydydx=\frac{4}{3}[/URL]

but for [PLAIN]http://latex.codecogs.com/gif.latex?\oint%20Mdx+ndy+pdz if i get x=cost ,y=sint and z=0 the answer is [URL]http://latex.codecogs.com/gif.latex?\int_{0}^{\pi/2}x^2dx+xydy-z^2dz=0[/URL] but i can't find my problem??

i should equal [PLAIN]http://latex.codecogs.com/gif.latex?\oint%20Mdx+ndy+pdz

with [PLAIN]http://latex.codecogs.com/gif.latex?\int%20\int%20curlF.n.d\sigma

i know : curlF=(0,0,y) and n=(x,y,z) and [URL]http://latex.codecogs.com/gif.latex?d\sigma%20=\frac{dxdy}{z}[/URL] and [PLAIN]http://latex.codecogs.com/gif.latex?\int%20\int%20curlF.n.d\sigma = [URL]http://latex.codecogs.com/gif.latex?\int_{-1}^{1}\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}ydydx=\frac{4}{3}[/URL]

but for [PLAIN]http://latex.codecogs.com/gif.latex?\oint%20Mdx+ndy+pdz if i get x=cost ,y=sint and z=0 the answer is [URL]http://latex.codecogs.com/gif.latex?\int_{0}^{\pi/2}x^2dx+xydy-z^2dz=0[/URL] but i can't find my problem??

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