散度問題
題目(這是某校內期考題)
a＞0,b跟c屬於R,b＜c,S is part of cylinder S =｛﹙x,y,z﹚,x^2+y^2=a^2,b≦z≦c｝
which is oriented with the unit normal pointing toward z-axis.
Evaluate the surface intergral I =∫∫x^3 dydz + x^2 y dzdx + x^2 z dxdy?
6
以下是答案的某一步
∫∫∫5x^2 dxdydz = -I + ∫∫ x^2 z dxdy + ∫∫ x^2 z dxdy
I 6 x^2+y^2≦a,z=c x^2+y^2≦a,z=b
有誰可以解釋這這一步是怎出來的嗎
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