Let F = yi + xjx2 + y2 .(a) Calculate curl F . What is the domain of curl F (b) Find the

Chapter 20, Problem 46

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Let F = yi + xjx2 + y2 .(a) Calculate curl F . What is the domain of curl F ?(b) Find the circulation of F around the unit circleC1 in the xy-plane, oriented counterclockwise whenviewed from above.(c) Find the circulation of F around the circle C2 in theplane z = 4 and with equation (x 3)2 + y2 = 1,oriented counterclockwise when viewed from above.(d) Find the circulation of F around the squareS with corners (2, 2, 0), (2, 2, 0), (2, 2, 0),(2, 2, 0), oriented counterclockwise when viewedfrom above.(e) Using your results to parts (b)(d) explain how, withno additional calculation, you can find the circulationof F around any simple closed curve in the xyplane,provided it does not intersect the z-axis. (Asimple closed curve does not cross itself.)