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(a) Evaluate feay'ds with C being the right half of the circle + y - 16. Does it depend on orientation? (b) Compute Jo(r+ 2y)dr + dy with C consisting of line segments from (3,0) to (2, 1) and (2. 1) to (0, 0). (e) Compute the work dlone by the force field F(r. v. 2)- (sin y. z CON V+ cos 2, -V sin z) on a particle along the curve

(a) Evaluate feay'ds with C being the right half of the circle + y - 16. Does it depend on orientation? (b) Compute Jo(r+ 2y)dr + dy with C consisting of line segments from (3,0) to (2, 1) and (2. 1) to (0, 0). (e) Compute the work dlone by the force field F(r. v. 2)- (sin y. z CON V+ cos 2, -V sin z) on a particle along the curve

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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solve part (b) using Green's Theorm
Q2. Line Integral and Fundamental Theorem of Line Integral (a) Evaluate Lery'ds with C being the right half of the circle r + y = 16. Does it depend on orientation? (b) Compute Jer + 2y)dr +x*dy with C consisting of line segments from (3,0) to (2, 1) and (2, 1) to (0, 0). (c) Compute the work done by the force field F(2, y. 2) = (sin y, z cos y + cos 2,-y sin z) on a particle along the curve r(t) = (sin t, t, 2t) for 0SEST/2. Hint: Find a potential function. (d) Consider the vector field F(2, u) - i + tj. (1) Find its domain D and show that P, Q, on D. (ii) Compute directly the line integrals fe, F dr and le F. dr, where C, is the upper half of the unit circle from (-1,0) to (1,0) and C. is the lower half of the unit circle from (-1,0) to (1,0). (ii) Conclude that fe F dr is not independent of path and explain why this does not contradict the
Transcribed Image Text:Q2. Line Integral and Fundamental Theorem of Line Integral (a) Evaluate Lery'ds with C being the right half of the circle r + y = 16. Does it depend on orientation? (b) Compute Jer + 2y)dr +x*dy with C consisting of line segments from (3,0) to (2, 1) and (2, 1) to (0, 0). (c) Compute the work done by the force field F(2, y. 2) = (sin y, z cos y + cos 2,-y sin z) on a particle along the curve r(t) = (sin t, t, 2t) for 0SEST/2. Hint: Find a potential function. (d) Consider the vector field F(2, u) - i + tj. (1) Find its domain D and show that P, Q, on D. (ii) Compute directly the line integrals fe, F dr and le F. dr, where C, is the upper half of the unit circle from (-1,0) to (1,0) and C. is the lower half of the unit circle from (-1,0) to (1,0). (ii) Conclude that fe F dr is not independent of path and explain why this does not contradict the
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