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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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 25E
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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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