求∫(e∧xsiny-y)dx+(e∧xcosy-1)dy,其中L为点A（2，0）到点B（0,0）的圆周x^2+y^2=2x
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补上线段y = 0
则令P = e^xsiny - y，dP/dy = e^xcosy - 1
Q = e^xcosy - 1，dQ/dx = e^xcosy
∫_L (e^xsiny - y) dx + (e^xcosy - 1) dy
= ∫∫_D [(e^xcosy) - (e^xcosy - 1)] dxdy
= ∫∫_D dxdy
= 1/2 • π(1)²
= π/2
则令P = e^xsiny - y，dP/dy = e^xcosy - 1
Q = e^xcosy - 1，dQ/dx = e^xcosy
∫_L (e^xsiny - y) dx + (e^xcosy - 1) dy
= ∫∫_D [(e^xcosy) - (e^xcosy - 1)] dxdy
= ∫∫_D dxdy
= 1/2 • π(1)²
= π/2
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