Unformatted text preview: segments) to be the sum of the areas swept out over each of the segments making up the path. 11. (a) Show that the area swept out by DP as P travels along an oriented triangle equals the signed area of the triangle: that is, show that σ ( ABC ) A ( △ ABC ) = σ ( DAB ) A ( △ DAB )+ σ ( DBC ) A ( △ DBC )+ σ ( DCA ) A ( △ DCA ) . ( Hint: This can be done geometrically. Consider three cases: D lies outside, inside, or on △ ABC . See ±igure 1.47 .) (b) Show that the area swept out by O P as P moves along the line segment from ( x ,y ) to ( x 1 ,y 1 ) is 1 2 v v v v x y x 1 y 1 v v v v ....
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 Fall '08
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 Calculus, Vectors, Line segment, σ, line segment AB

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