(a) Let F = [cos (x), e-Y, e-2²], C: r = [2t, t², 3t], calculate the integral S. F(r) · dr based on (x, y, z) starting from (0, 0, 0) to (4, 4, 6). Let F = + x*y, -y*], C: r= [t², t"], (b) (i) calculate these integrals S, F(r)· dr based on (x, y) from (0, 0) to (1, 1) in terms of n; (ii) work out the values of the above line integrals by setting n = 0,1 and +o (iii) based on result from (ii), state whether above line integral is path independence or not. (“yes" or "no")
(a) Let F = [cos (x), e-Y, e-2²], C: r = [2t, t², 3t], calculate the integral S. F(r) · dr based on (x, y, z) starting from (0, 0, 0) to (4, 4, 6). Let F = + x*y, -y*], C: r= [t², t"], (b) (i) calculate these integrals S, F(r)· dr based on (x, y) from (0, 0) to (1, 1) in terms of n; (ii) work out the values of the above line integrals by setting n = 0,1 and +o (iii) based on result from (ii), state whether above line integral is path independence or not. (“yes" or "no")
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 b part
![(a)
Let F = [cos (x), e¬y, e-2²], C: r = [2t, t², 3t], calculate the integral S.F(r) · dr based on
(x, y, z) starting from (0, 0, 0) to (4, 4, 6).
(b)
+ x*y, -y, C: r = [t°, t"],
Let F =
(i) calculate these integrals S. F(r) · dr based on (x, y) from (0, 0) to (1, 1) in terms of n;
(ii) work out the values of the above line integrals by setting n = 0,1 and +o
(iii) based on result from (ii), state whether above line integral is path independence or not. (“yes" or
“no")](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6c94f8b-e4e8-42e0-9e7f-ba60326e1e30%2Ff47e02cb-b389-4ce1-af24-aca59df69f43%2Fuu4e24n_processed.png&w=3840&q=75)
Transcribed Image Text:(a)
Let F = [cos (x), e¬y, e-2²], C: r = [2t, t², 3t], calculate the integral S.F(r) · dr based on
(x, y, z) starting from (0, 0, 0) to (4, 4, 6).
(b)
+ x*y, -y, C: r = [t°, t"],
Let F =
(i) calculate these integrals S. F(r) · dr based on (x, y) from (0, 0) to (1, 1) in terms of n;
(ii) work out the values of the above line integrals by setting n = 0,1 and +o
(iii) based on result from (ii), state whether above line integral is path independence or not. (“yes" or
“no")
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