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Given that C₁ is defined by the circle x² + (y−1)² = 4 traced counterclockwise and C₂ be the trapezoid traced clockwise with vertices at (-5,3), (3,4), (3,-7) and (-5,-1). Consider the force field F(x, y) = (e¹-³ – 4y,4x −e²-³). a. By parametrizing C₁, find the work done by the force field F in moving an object around C₁ exactly once.

Given that C₁ is defined by the circle x² + (y−1)² = 4 traced counterclockwise and C₂ be the trapezoid traced clockwise with vertices at (-5,3), (3,4), (3,-7) and (-5,-1). Consider the force field F(x, y) = (e¹-³ – 4y,4x −e²-³). a. By parametrizing C₁, find the work done by the force field F in moving an object around C₁ exactly once.

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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Given that C₁ is defined by the circle x² + (y−1)² = 4 traced counterclockwise and C₂ be the trapezoid traced clockwise with vertices at (-5,3), (3,4), (3,-7) and (-5,-1). Consider the force field F(x,y)=(e--4y,4x-e²-). a. By parametrizing C₁, find the work done by the force field in moving an object around C₁ exactly once.
Transcribed Image Text:Given that C₁ is defined by the circle x² + (y−1)² = 4 traced counterclockwise and C₂ be the trapezoid traced clockwise with vertices at (-5,3), (3,4), (3,-7) and (-5,-1). Consider the force field F(x,y)=(e--4y,4x-e²-). a. By parametrizing C₁, find the work done by the force field in moving an object around C₁ exactly once.
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Let R be the region outside C₁ but inside C₂, compute F.dR using the idea of Green's Theorem on C:= C₁ C₂ and R.
Transcribed Image Text:Let R be the region outside C₁ but inside C₂, compute F.dR using the idea of Green's Theorem on C:= C₁ C₂ and R.
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Use exponents and grouping symbol as well. Thank you. 

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