VC4.5

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Here the curve C is y={\sqrt  {1-x^{2}}}\, or x^{2}+y^{2}=1\, which lies on xy-plane.Again,in xy-plane,r=xi+yj,dr=dxi+dyj\,

Therefore \int _{{C}}F\cdot \,dr=\int _{{C}}(\cos yi-x\sin yj)\cdot (dxi+dyj)=\int _{{1,0}}^{{0,1}}(\cos ydx-x\sin ydy)=[x\cos y]_{{1,0}}^{{0,1}}=0-1=-1\,

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