Let F = (4z+4x³)i + (4y + 4z + 4 sin(y³))j+ (4x + 4y + 4eˣ³) k (a) Find curl F. (b) What does your answer to part (a) tell you

Question

Let F = (4z+4x³)i + (4y + 4z + 4 sin(y³))j+ (4x + 4y + 4eˣ³) k
(a) Find curl F.
(b) What does your answer to part (a) tell you about ∫F.dr where C is the circle 
                                                                                       c
(x-10)²+(y-25)²=1 in the xy-plane, oriented clockwise?    
(c) If C is any closed curve,what can you say about∫ F.dr?
                                                                                    c
(d) Now let C be the half circle (x-10)² + (y-25)²=1 in the xy-plane with y> 25, traversed from (11, 25) to (9, 25). Find ∫F .dr by using your result from (c) and 
                                                                  c
considering C plus the line segment connecting the endpoints of C.

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