Show clear full work 1. Suppose that F ds 5, where F is an arbitrary vector fiel

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1. Suppose that F ds 5, where F is an arbitrary vector field and Cis the circle of radius 1, centered at the origin, starting at (1,0) and traveling counterclockwise back to (1,0). Determine whether each of the following statement is True or False. Provide a justification for each answer. 12 points each) (a) T F.ds- 5, where Ci is the same curve as c but starting at (0,1) and traveling counterclockwise back to (0,1). (b) T ds m -5, where Ca is the same curve as C, starting at (1,0), but traveling clockwise back to (1,0) (c) F.ds T, where cs is a semi-circle of radius 1, centered at the origin, starting at (1,0) and traveling counterclockwise to (-1,0) (d) F.ds 10, where ci is the circle of radius 2, centered at the origin, starting at (2,0) and traveling counterclockwise back to (2,00. (e) F. ds 10, where C5 is the circle parametrized by c(t) (cos(2t), sin(2t)), 0 St S 2T.

Explanation / Answer

a)True: exactly same path and same vector field.

b) false : path independent

c)false : algebraic sum of two sum will be total, the function may or may not be symmetric

d) correct : it's just advancing the area.

e)False : radius is still 1.

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