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Show that the force field F(x, y, z) = (81xz)i + (1 −6yz³)j + (42²-9y²22) k is conservative and find its potential function. Hence find the work done by F(x, y, z) in moving an object from (1,4,0) to (3, 4, 1) and then to (2,0,3). If C is the boundary of the region bounded by the curves y 1² and y = 1+2, use Green's theorem to evaluate (2y + e√²) dr + (3x + cos (y²)) dy.

Show that the force field F(x, y, z) = (81xz)i + (1 −6yz³)j + (42²-9y²22) k is conservative and find its potential function. Hence find the work done by F(x, y, z) in moving an object from (1,4,0) to (3, 4, 1) and then to (2,0,3). If C is the boundary of the region bounded by the curves y 1² and y = 1+2, use Green's theorem to evaluate (2y + e√²) dr + (3x + cos (y²)) dy.

Advanced Engineering Mathematics
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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Show that the force field F(x, y, z) = (81xz)i + (1 −6yz³)j + (42²-9y²22) k is conservative and find its potential function. Hence find the work done by F(x, y, z) in moving an object from (1,4,0) to (3, 4, 1) and then to (2,0,3). If C is the boundary of the region bounded by the curves y 1² and y = 1+2, use Green's theorem to evaluate (2y + e√²) dr + (3x + cos (y²)) dy.
Transcribed Image Text:Show that the force field F(x, y, z) = (81xz)i + (1 −6yz³)j + (42²-9y²22) k is conservative and find its potential function. Hence find the work done by F(x, y, z) in moving an object from (1,4,0) to (3, 4, 1) and then to (2,0,3). If C is the boundary of the region bounded by the curves y 1² and y = 1+2, use Green's theorem to evaluate (2y + e√²) dr + (3x + cos (y²)) dy.
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