(b) Assume that F(x, y, z)= ei+zej + (z + 1)ek is a vector field defined on a smooth curve C given by r(t) ti+t²j+t³k for 0 ≤ t ≤ 1. -
(b) Assume that F(x, y, z)= ei+zej + (z + 1)ek is a vector field defined on a smooth curve C given by r(t) ti+t²j+t³k for 0 ≤ t ≤ 1. -
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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Please help with (b)
Transcribed Image Text:(b) Assume that F(x, y, z)= ei+zej + (z + 1)e-k is a vector field defined on a
smooth curve C given by r(t) = ti+t2j+t³k for 0 ≤ t ≤ 1.
Page 1 of 2
(i) Using the fundamental theorem of calculus, evaluate the line integral
Jc F. dr.
(ii) Show whether foF. dr is independent of path.
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