Show that / F. dr is independent of its path, given that F(x, y, 2) = ( : 2) i+ tan-lr j+ k. 1+ 22 + tan 1+ x2 Hence, find the potential function of F and then evaluate the work done by F moving an object along the smooth curve C, the line segment from (1,0, –1) to (0,0, 0) then along the parabola z = y°, x = 0 to (0, –1, 1). %3D

Show that / F. dr is independent of its path, given that F(x, y, 2) = ( : 2) i+ tan-lr j+ k. 1+ 22 + tan 1+ x2 Hence, find the potential function of F and then evaluate the work done by F moving an object along the smooth curve C, the line segment from (1,0, –1) to (0,0, 0) then along the parabola z = y°, x = 0 to (0, –1, 1). %3D

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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Differential Equations

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Question

b) Show that
F. dr is independent of its path, given that
F(x, y, 2) = ( ;
-1
+ tan
-1
i+ tan
xj+
1+ z2
k.
1+ x²
Hence, find the potential function of F and then evaluate the work done
by F moving an object along the smooth curve C', the line segment from
(1,0, – 1) to (0,0, 0) then along the parabola z = y°, x = 0 to (0, – 1, 1).

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