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(a) Given that N = (3yz-2)i + (3xz-2)j +(3xy-2)k (i) show that N is conservative; (ii) find n(x, y, z) such that Ñ- Vn; (2,3,2) Hence or otherwise, evaluate (2,3 (3yz-2)dx +(3xz− 2)dy+ (3xy− 2)dz . J(0,2,0) !!!

(a) Given that N = (3yz-2)i + (3xz-2)j +(3xy-2)k (i) show that N is conservative; (ii) find n(x, y, z) such that Ñ- Vn; (2,3,2) Hence or otherwise, evaluate (2,3 (3yz-2)dx +(3xz− 2)dy+ (3xy− 2)dz . J(0,2,0) !!!

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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(a) Given that N = (3yz-2)i +(3xz-2)j+(3xy-2)k (i) show that N is conservative; (ii) find n(x, y, z) such that N-Vn; Hence or otherwise, evaluate (232) (3yz-2)dx+(3xz −2)dy+ (3xy-2)dz . J(0, 2,0) !!! (b) Let E be the part of the solid x² + y² < (5-z)² with 0≤z≤3, where S is the boundary of E and F = 1xi+yj. Calculate the volume of the solid.
Transcribed Image Text:(a) Given that N = (3yz-2)i +(3xz-2)j+(3xy-2)k (i) show that N is conservative; (ii) find n(x, y, z) such that N-Vn; Hence or otherwise, evaluate (232) (3yz-2)dx+(3xz −2)dy+ (3xy-2)dz . J(0, 2,0) !!! (b) Let E be the part of the solid x² + y² < (5-z)² with 0≤z≤3, where S is the boundary of E and F = 1xi+yj. Calculate the volume of the solid.
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