(a) If C is the line segment connecting the point (x,, y,) to the point (x,, Y½), find the following. x dy – y dx (b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Y2), ..., (xp Y), find the area of the polygon. O A (x2Y1 - ×1¥2) + (X3V2 - X2Y3) + ·…· + (X,Yn-1 – Xn-1Vn) + (×1V, – X„Y1) ... 4 = =(xxv2 + x2Y1) + (x2Y3 + X3Y2) + •·· + (x, - 1Yn + XnYn - 1) + (x„V1 + ×q¥n}] (xqY2 - x2yq) + (xzy3 - X3Y2) + •·· + (x, - 1Yn - x,Yn - 1) + (x,V1 – x;Yn +...+ O A = (x,V2 - x2Y;) – (X2Y3 - X3V2) – - (xp – 1Yn – x,Yn - 1) + (x„V1 - xqY½)| O A = (X1Y2 - X2Y1) + (×2Y3 - X3V2) + … + (x, - 1Yn – X„Yn – 1) + (x„Y1 - ×1V) ... (c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 1), and (-1, 1).
(a) If C is the line segment connecting the point (x,, y,) to the point (x,, Y½), find the following. x dy – y dx (b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Y2), ..., (xp Y), find the area of the polygon. O A (x2Y1 - ×1¥2) + (X3V2 - X2Y3) + ·…· + (X,Yn-1 – Xn-1Vn) + (×1V, – X„Y1) ... 4 = =(xxv2 + x2Y1) + (x2Y3 + X3Y2) + •·· + (x, - 1Yn + XnYn - 1) + (x„V1 + ×q¥n}] (xqY2 - x2yq) + (xzy3 - X3Y2) + •·· + (x, - 1Yn - x,Yn - 1) + (x,V1 – x;Yn +...+ O A = (x,V2 - x2Y;) – (X2Y3 - X3V2) – - (xp – 1Yn – x,Yn - 1) + (x„V1 - xqY½)| O A = (X1Y2 - X2Y1) + (×2Y3 - X3V2) + … + (x, - 1Yn – X„Yn – 1) + (x„Y1 - ×1V) ... (c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 1), and (-1, 1).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![(a) If C is the line segment connecting the point (x, Y1) to the point (X2, Y2), find the following.
x dy – y dx
(b) If the vertices of a polygon, in counterclockwise order, are (x,, Y1), (x2, Y2), ..., (Xp Yn), find the area of the polygon.
O A = (x2V1 - X1¥2) + (×3V2 - X2V 3) + ·…· + (x,Yn-1 - xn-1Yn) + (×1Yn - x
2
O A =
+ x2y1) + (x2y3 + x3¥2) + ·.. + (x, – 1ýn + X„Yn – 1) + (x,Y1 + x1Vn)
1
O A =(x,Y2 - X2Y2) + (xzY3 = X3Y2) + ·· + (x, - 1'n – x„Yn - 1) + (x,V1 - X4Yn}]
1
O A = (x,y2 - ×2Y1) - (X2Y3 - X3Y2) –. - (x, - 1Yn – xnYn - 1) + (x„Y1 - X1Vn]
O A = (x,y2 - X2Y1) + (x2Y3 - X3V2) + .. + (x, - 1n - x,Yn - 1) + (x,Y1 - ×1¥n)
(c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 1), and (-1, 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F541a3947-3d35-41c4-b89d-c67bcfa121c1%2Ff2023f8e-eeab-44f1-8197-0a10208e5952%2Fq2e6fp_processed.png&w=3840&q=75)
Transcribed Image Text:(a) If C is the line segment connecting the point (x, Y1) to the point (X2, Y2), find the following.
x dy – y dx
(b) If the vertices of a polygon, in counterclockwise order, are (x,, Y1), (x2, Y2), ..., (Xp Yn), find the area of the polygon.
O A = (x2V1 - X1¥2) + (×3V2 - X2V 3) + ·…· + (x,Yn-1 - xn-1Yn) + (×1Yn - x
2
O A =
+ x2y1) + (x2y3 + x3¥2) + ·.. + (x, – 1ýn + X„Yn – 1) + (x,Y1 + x1Vn)
1
O A =(x,Y2 - X2Y2) + (xzY3 = X3Y2) + ·· + (x, - 1'n – x„Yn - 1) + (x,V1 - X4Yn}]
1
O A = (x,y2 - ×2Y1) - (X2Y3 - X3Y2) –. - (x, - 1Yn – xnYn - 1) + (x„Y1 - X1Vn]
O A = (x,y2 - X2Y1) + (x2Y3 - X3V2) + .. + (x, - 1n - x,Yn - 1) + (x,Y1 - ×1¥n)
(c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 1), and (-1, 1).
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