Show that F. dr is independent of its path, given that F(л, у, 2) — + tan 1+x² 2) i+ tanrj+ k. 1+2² 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).

Show that F. dr is independent of its path, given that F(л, у, 2) — + tan 1+x² 2) i+ tanrj+ k. 1+2² 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).

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

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

b) Show that
F. dr is independent of its path, given that
F(x, y, z) =
+ tan-z) i+ tan¬xj+
+ x2
k.
1+ 22
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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