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a. Show that the line integral Sc (yz - 2z) dx + (xz+3) dy + (xy - 2x) dz is independent of the path. b. Evaluate the line integral Sc (yz — 2z) dx + (xz + 3) dy + (xy – 2x) dz, where C' is any sectionally smooth simple curve from the point (-1, 0, 1) to the point (0, -2, 4). (Hint: Find a potential function for the vector field.)

a. Show that the line integral Sc (yz - 2z) dx + (xz+3) dy + (xy - 2x) dz is independent of the path. b. Evaluate the line integral Sc (yz — 2z) dx + (xz + 3) dy + (xy – 2x) dz, where C' is any sectionally smooth simple curve from the point (-1, 0, 1) to the point (0, -2, 4). (Hint: Find a potential function for the vector field.)

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 line integral Sc (yz — 2z) dx + (xz + 3) dy + (xy – 2x) dz is independent of the path. a. b. Evaluate the line integral Sc (yz — 2z) dx + (xz + 3) dy + (xy − 2x) dz, where C is any sectionally smooth simple curve from the point (-1, 0, 1) to the point (0, -2, 4). (Hint: Find a potential function for the vector field.)
Transcribed Image Text:Show that the line integral Sc (yz — 2z) dx + (xz + 3) dy + (xy – 2x) dz is independent of the path. a. b. Evaluate the line integral Sc (yz — 2z) dx + (xz + 3) dy + (xy − 2x) dz, where C is any sectionally smooth simple curve from the point (-1, 0, 1) to the point (0, -2, 4). (Hint: Find a potential function for the vector field.)
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