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(a) If C is the line segment connecting the point (x,, Y,) to the point (x2, Y2), find the following. x dy - y dx

(a) If C is the line segment connecting the point (x,, Y,) to the point (x2, Y2), find the following. x dy - y dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Needed to be solved correclty in 1 hour completely and get the thumbs up please show neat and clean work.box answer should be right
(a) If C is the line segment connecting the point (x,, y1) to the point (x2, Y2), find the following. х dy — у dx (b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (X2, Y½),. (xp Yn), find the .... area of the polygon. O A = 2 (X1V2 + X2V1) + (x2V3 + X3Y2) + ·… · + (xn – 1V+ XnYn – 1) + (xnY 1 + X1. O A = (x>Y1 - X,¥2) + (X3V2 - X2Y3) + ·… · + (x,Yn-1 – Xn-1Yn) + (X,Yn - X,V1)| O A 2 =(×1V2 – x2Y1) – (X2V3 – X3¥2) – (Xn - 1Yn – XnYn - 1) + (x„y1 – X1V½)| O A = (x1V2 - X2V1) + (x2V3 - X3V2) + ·. + (x, – 1Yn – X,Y - 1) + (x,V1 – X1Yn}| O A = (X1V2 – X2Y 1) + (x2Y3 - X3Y2) + •· · + (X, – 1Yn – XnYn - 1) + (X,Y1 – ×1V½) (c) Find the area of the pentagon with vertices (0, 0), (3, 1), (1, 2), (0, 1), and (-2, 1).
Transcribed Image Text:(a) If C is the line segment connecting the point (x,, y1) to the point (x2, Y2), find the following. х dy — у dx (b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (X2, Y½),. (xp Yn), find the .... area of the polygon. O A = 2 (X1V2 + X2V1) + (x2V3 + X3Y2) + ·… · + (xn – 1V+ XnYn – 1) + (xnY 1 + X1. O A = (x>Y1 - X,¥2) + (X3V2 - X2Y3) + ·… · + (x,Yn-1 – Xn-1Yn) + (X,Yn - X,V1)| O A 2 =(×1V2 – x2Y1) – (X2V3 – X3¥2) – (Xn - 1Yn – XnYn - 1) + (x„y1 – X1V½)| O A = (x1V2 - X2V1) + (x2V3 - X3V2) + ·. + (x, – 1Yn – X,Y - 1) + (x,V1 – X1Yn}| O A = (X1V2 – X2Y 1) + (x2Y3 - X3Y2) + •· · + (X, – 1Yn – XnYn - 1) + (X,Y1 – ×1V½) (c) Find the area of the pentagon with vertices (0, 0), (3, 1), (1, 2), (0, 1), and (-2, 1).
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