Question: Let C be the curve parameterized by r ( t )=cos( t ) i +sin( t ) j +[cos2( t ) a sin2( t )]

Let C be the curve parameterized by r(t)=cos(t) i +sin(t)j+[cos2(t)asin2(t)]k, 0t2, where a is a constant. For which value(s) of a is the circulation of the field defined by F(x,y,z)=[sin(x2)+z]i+[cos(y2)z]j+axyk around C maximal?

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