Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²))j + (3x + 4y +6e²² (a) Find curl F. curl F - <0,0,0> (b) What does your answer to part (a) tell you about SF. dr where C' is the circle (x − 15)² + (y - 10)² = 1 in the xy-plane, oriented clockwise? ScFdr = 0 (c) If C is any closed curve, what can you say about ScF. dr? SF.dr = 0 (d) Now let C be the half circle (x − 15)² + (y — 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. ScF. dr =

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