calculate the line integral for a vector field F= -xy⋅j over a circle which is c(t)=costi+sintj,(adsbygoogle = window.adsbygoogle || []).push({});

so I used x=cost y=sint and ∫(0 to 2pi) -(sintcost)(cost)dt=(cos^3(2pi)-cos^3(o))/3=0 now here is the problem, if this enclosed line integral is zero then why is the vector field not conservative????

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# I Evaluation of a line integral

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