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

q) a)Parametrize the following paths from (−2, 0) to (2, 0) in the 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 three parametrizations.)
• A path counterclockwise along a circle centered at the origin.

b) Compute the integral F⃗ · d⃗r along each of these paths for F⃗ (x, y) = (−y, x).

c) Compute the integral G⃗ · d⃗r along each of these paths for G⃗ (x, y) = (y2, 2xy).

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

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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