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2. Solve the following showing full and complete procedure a) Evaluate the integral either directly or using Green's theorem: f (x - y)dx + (x + y)dy where C is the circle with center in the origin and radius 2 O b) Use Green's theorem to evaluate C Fodr where F(x,y) = (ycosx - xysinx, xy + xcosx)

2. Solve the following showing full and complete procedure a) Evaluate the integral either directly or using Green's theorem: f (x - y)dx + (x + y)dy where C is the circle with center in the origin and radius 2 O b) Use Green's theorem to evaluate C Fodr where F(x,y) = (ycosx - xysinx, xy + xcosx)

Calculus: Early Transcendentals
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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show full and complete procedure HANDWRITTEN only. Please answer parts a), b) and c) as they are subparts of the same question 

2. Solve the following showing full and complete procedure a) Evaluate the integral either directly or using Green's theorem: O ¨(x − y)dx + (x + y)dy where C is the circle with center in the origin and radius 2 b) Use Green's theorem to evaluate F o dr where F(x,y) = (ycosx - xysinx, xy + xcosx) and C is the triangle from (0,0) to (2,0) to (0,4) to (0,0) c) Use Stoke's theorem to evaluate F o dr where F(x,y,z) = x²zi + xy²j + z²k and C is с the curve of intersection of the plane x+y+z=1 and the cylinder x² + y² = 9 oriented counterclockwise as viewed from above
Transcribed Image Text:2. Solve the following showing full and complete procedure a) Evaluate the integral either directly or using Green's theorem: O ¨(x − y)dx + (x + y)dy where C is the circle with center in the origin and radius 2 b) Use Green's theorem to evaluate F o dr where F(x,y) = (ycosx - xysinx, xy + xcosx) and C is the triangle from (0,0) to (2,0) to (0,4) to (0,0) c) Use Stoke's theorem to evaluate F o dr where F(x,y,z) = x²zi + xy²j + z²k and C is с the curve of intersection of the plane x+y+z=1 and the cylinder x² + y² = 9 oriented counterclockwise as viewed from above
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