Question: (a) Let C be the line segment joining (x, y) and (x, y). Show that c -y dx + x dy = XY2 - Xy.

(a) Let C be the line segment joining (x₁, y₁) and (x₂, y₂). Show that ∫c -y dx + x dy = X₁Y2 - X₂y₁.

(b) Let (x₁, y₁), (x₂, y₂),..., (xn, yn) be the vertices of a polygon. Prove that the area enclosed is

1/[(xxy) + (x V3 X3Y) + + +. (xn-1n-XnYn-1) + (xy xy)].

1/[(xxy) + (x V3 X3Y) + + +. (xn-1n-XnYn-1) + (xy xy)]. - -

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