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1. Find the work done by F(x, y, z) = (-y,–x, z) on a particle that moves along the curve R(t) (2 cos t, 2 sin t, t), where 0

1. Find the work done by F(x, y, z) = (-y,–x, z) on a particle that moves along the curve R(t) (2 cos t, 2 sin t, t), where 0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 17EQ
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1. Find the work done by F(x, y, z) (2 cos t, 2 sin t, t), where 0<t < . (-y, -x, z) on a particle that moves along the curve R(t) (4 points) 2. Use the Fundamental Theorem of Line Integrals to evaluate fo F.dR, where F(r, y) = (x²y² – 3.r,r³y) and C is the line segment from (-1,0) to (0,0) followed by the line segment from (0,0) to (1,1). (4 points) 3. Use Green's Theorem to evaluate | (e* + y)dx + (sin y – x²)dy where C is the boundary of the region bounded by y= 0 and y = V9 – x2. (4 points)
Transcribed Image Text:1. Find the work done by F(x, y, z) (2 cos t, 2 sin t, t), where 0<t < . (-y, -x, z) on a particle that moves along the curve R(t) (4 points) 2. Use the Fundamental Theorem of Line Integrals to evaluate fo F.dR, where F(r, y) = (x²y² – 3.r,r³y) and C is the line segment from (-1,0) to (0,0) followed by the line segment from (0,0) to (1,1). (4 points) 3. Use Green's Theorem to evaluate | (e* + y)dx + (sin y – x²)dy where C is the boundary of the region bounded by y= 0 and y = V9 – x2. (4 points)
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