Re: [積分] 請教一題向量積分@@
※ 引述《a039333780 (阿國~)》之銘言：
: Let C be a simple colsed smooth curve in the plane x+2y+2z=2
: 求環積分Ｓ3ydx-2zdy+xdz
: 我算到最後是1去做green
: 可是green的上下界...我就不會找了><
: (這題是98台聯大最後一題= =)
既然有答案了 我就RE一下
let x=u y=v z=1-u/2-v
F=(3y,-2z,x) curl F=(2,-1,-3)
let f(x,y,z)=x+2y+2z-2
N=grad f =(1,2,2) 取單位向量n=(1/3,2/3,2/3)
by stokes's theorem
∫∫F‧dr=∫∫(curl F)‧n dσ
=∫∫(2,-1,-3)‧(1/3,2/3,2/3) dσ
=-2s
我沒看清楚你答案是-2"曲面面積"所以就直接用dσ就可以了
我看了很多次 應該沒錯了
這題線積分直接算 他投影是三角形為片段平滑而且連續且具一階偏導數
所以STOKE 應該是可以用 只是線積分不好算
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◆ From: 140.117.198.78
※ 編輯: midarmyman 來自: 140.117.198.78 (04/23 17:10)
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※ 編輯: midarmyman 來自: 140.117.198.78 (04/25 11:30)
※ 編輯: midarmyman 來自: 140.117.198.78 (04/25 11:50)
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