Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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below math question part C
Transcribed Image Text:(a) If C is the line segment connecting the point (x1, Y1) to the point (x2, y2), find the following.
х dy — у dx
(b) If the vertices of a polygon, in counterclockwise order, are (X1, Y1), (x2, Y2),
(Xn, Yn), find the area of the polygon.
...
A =
(X1Y2 - X2V1) + (x2Y3 - X3y2) + · ..
+ (Xn – 1Yn – XnYn – 1) + (XnY1 - X1Yn)
A = (X1V2 – X2V1) + (×2V3 – X3Y2) +
+ (xn - 1Ул — ХnYn - 1) + (xnУ1 - X1Уп)
A
(x2V1 – X1Y2) + (X3Y2 – X2V3) +
+ (XnYn-1 – Xn-1Yn) + (x1Yn – xXnY1)
O A =
(X1Y2 + X2Y1) + (X2V3 + X3V2) +
+ (Xn – 1Yn + XnYn – 1) + (XnY1 + X1Yn)
= (x1Y2 – X2Y1) – (x2Y3 – X3Y2)
-(xn – 1Yn – XnYn – 1) + (xnY1 – x1Yn)
A =
(c) Find the area of the pentagon with vertices (0, 0), (4, 1), (1, 3), (0, 2), and (-1, 1).
H|N -|n 2
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