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?
