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  3. q) a)parametrize the following paths from (?2, 0)

q) a)Parametrize the following paths from (?2, 0) to (2, 0) in the xy-plane: • A straight...

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Advance Math

q) a)Parametrize the following paths from (?2, 0) to (2, 0) inthe xy-plane:
• A straight line path.
• A path consisting of three lines: (?2, 0) to (?2, 2), from (?2,2) to (2, 2), and from (2, 2) to (2, 0). (Give threeparametrizations.)
• A path counterclockwise along a circle centered at theorigin.

b) Compute the integral F? · d?r along each of these paths forF? (x, y) = (?y, x).

c) Compute the integral G? · d?r along each of these paths forG? (x, y) = (y2, 2xy).

d)What do you notice about your answers to parts (b) and (c)?Are either F? or G? a gradient field?

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