Question: Evaluate F(r) . dr counterclockwise around the boundary C C of the region R by Green's theorem, where 1. F = [y, -x], C the

Evaluate F(r) . dr counterclockwise around the boundary C C of the region R by Green's theorem, where 1. F = [y, -x], C the circle x + y = 1/4 2. F = [6y , 2x - 2y*], R the square with vertices + (2, 2), + (2, -2) 3. F = [x2ey, y e"], R the rectangle with vertices (0, 0), (2, 0), (2, 3), (0, 3) 4. F = [x cosh 2y, 2x sinh 2y], R: x Sy S x 5. F = [x2 + y2, x2 - y"], R: 1sys2-x 6. F = [cosh y, - sinh x], R: 1 E x 3, x Sy = 3x

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