(1) Use Green's Theorem to evaluate the line integral fa unit circle orientated counterclockwise. (2) Use Green's Theorem to evaluate the line integral f xy dx + y dy where C is the (Inx + y) dxx²dy over the - rectangle in the xy-plane with vertices at (1, 1), (3, 1), (1, 4), and (3, 4). (3) If C is a simple closed curve, what is the value of y dx + x dy? = (4) Use Green's Theorem to evaluate the line integral of the vector field F(x, y) = 3+ around the unit square (the square in the xy-plane with vertices at (0,0), (0, 1), (1, 0), and (1, 1)) orientated clockwise. (5) Let A be the region in the xy-plane between the circles a² + y² = 1 and r²+ y² = 4. Let F(x, y) = (-y³, 2). Use Green's Theorem to evaluate for F. ds where C is the boundary of A with the outer circle orientated counterclockwise and the inner circle orientate clockwise (in other words, with the entire boundary of A orientated in the positive direction). (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use Green's Theorem to compute the area above the x-axis and under one arch of the cycloid given parametrically by x = f(t)=t-sint, y = g(t) = 1 cost, 0≤t≤2π.