This preview shows page 1. Sign up to view the full content.
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 ( ABC ) A ( ABC ) = ( DAB ) A ( DAB )+ ( DBC ) A ( DBC )+ ( 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 ....
View
Full
Document
This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Vectors

Click to edit the document details