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Problem 7.) Let C be the line segment joining the points (x1, y1) and (x2, 32) in R2. Prove that foxdy - y dx = Tly2 - x2y1.) Suppose further that...

Real analysis problem that I think uses Green's theorem.



Aug2008-7.png

Aug2008-7.png

Problem 7.
(a.) Let C be the line segment joining the points
(x1, y1) and (x2, 32) in R2.
Prove that foxdy - y dx = Tly2 - x2y1.
(b.) Suppose further that (x1, y1), . . ., (In, yn)
are vertices of a poly-
gon in R2, in counterclockwise order.
Prove that the area of the polygon is equal to
NIH
[(x192 - 1231) + (1293 - 1392)
+..+ (xny1 - T1yn )] .

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IMG_20190423_221408.jpg

The faranstrei equation of the lint digmint
gaining the Paint (MI) 91 ) and (x2 ) 92 ) in R2
x (*) - ( 1 -*)x) + tuz
y = (i-*)yitty2 uhw oct 31
C
Sadly- ydx = hit - 9172
dx = x'(t) dt
Hinu lrnel...

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