[理工] [工數]-線積分
Let C be a path on the paraboloid x^2+y^2-z=0 from the initial point
(1,0,1) to the terminal point (0,1,1);otherwise,C is arbitary.
(a)What is the value of the line integral
-ydx + xdy +zdz
∫ _________________
C along the path C ? Is it independent of path ?
x^2+y^2
答案當中出現了下面這個式子
-1 y -1 y │(0,1,1) π π
∫ d(tan ---) + dz = tan --- + z │ = (---- -1) - (0-1) = ----
C x x │(1,0,1) 2 2
可是我做積分時
x -1 y
在 ∫--------dy 時 積分出 tan --- 這一項
C x^2+y^2 x
不過
-y -1 x
在 ∫--------dx 時 卻積分出 -tan --- 這一項
C x^2+y^2 y
想請問一下是哪裡出現問題
謝謝!!
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