(a) Let C be the line segment joining (x, y) and (x, y). Show that c -y...
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(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
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1/[(x₁₂x₂y₁) + (x₂ V3 — X3Y₂) +・・・ + +. (xn-1n-XnYn-1) + (x₂y₁ − x₁y)]. - -
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