• Let S be the graph of f(z, y) = r² + y² – 2r + y for (1, y) E D = {(1,y) : r +y < 4 and z+ y 2 0}. • Let C, be the curve along the edge of the graph of f over the straight edge of D – starting in the second quadrant and ending in the fourth quadrant of D. • Let C2 be the curve along the edge of the graph of f over the circular edge of D – starting in the second quadrant and ending in the fourth quadrant of D. • Let F(r,y, 2) = (I, Y, Y – 2). 1. Compute fe F - dř.

Let S be the graph of f(x, y) = x² + y² - 2x + y for
(x, y) ∈ D = {(x, y) : x² + y² ≤ 4 and x + y ≥ 0}.

Let C₁ be the curve along the edge of the graph of f
over the straight edge of D – starting in the second
quadrant and ending in the fourth quadrant of D

• Let C₂ be the curve along the edge of the graph of f
over the circular edge of D – starting in the second
quadrant and ending in the fourth quadrant of D.

Let F(x, y, z) = ⟨x, y, y z⟩

Compute R:

C1 F¯ · dr¯.