Re: [理工] 工數向量作功
※ 引述《usa0204got (便秘)》之銘言：
: _ _ _
: if F = (x-y)/(x^2+y^2)i+(x+y)/(x^2+y^2)j is a defined in a simply
: connected domain R. evaluate the integral
: _ _
: ∫F‧dr
: c
: along the path r=2+(4Θ/5π) from (x1,y1)=(2,0)
: to (x2,y2)=(0,4),where r and Θ are polar coordinates .
: 卡在積分 感謝幫忙
Curl F = 0
(x-y)/(x^2+y^2) 對x偏積 => ψ1(x,y) = 0.5 ln│x^2 + y^2│ - arctan(x/y) + g(y)
(x+y)/(x^2+y^2) 對y偏積 => ψ2(x,y) = 0.5 ln│x^2 + y^2│ + arctan(y/x) + f(x)
∴ ψ(x,y) = 0.5 ln│x^2 + y^2│ + arctan(y/x) - arctan(x/y) + c
= 0.5 ln│x^2 + y^2│ + π/2 - 2arctan(x/y) + c
不知有沒有錯,大家討論一下
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