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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)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
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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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