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Let F(x, y, z) = (e" cos y, –e* sin y, 2). Evaluate the integral | F. dr, where C is the curve extending from the point (In 2, 7 /2, 1) to (–1, , 0).

Let F(x, y, z) = (e" cos y, –e* sin y, 2). Evaluate the integral | F. dr, where C is the curve extending from the point (In 2, 7 /2, 1) to (–1, , 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 vector field with component form F(x, y, z) = (P(x, y, z), Q(x, Y, z), R(x, y, z)) on R³ is conservative if ӘР ӘР de and dz ƏR ƏR dy' dz provided that certain "nice" conditions are met (which we assume). Let F(x, y, z) = (e² cos y, -e" sin y, 2). (c) Evaluate the integral F • dr, where C is the curve extending from the point (In 2, 7/2, 1) to (–1, , 0).
Transcribed Image Text:A vector field with component form F(x, y, z) = (P(x, y, z), Q(x, Y, z), R(x, y, z)) on R³ is conservative if ӘР ӘР de and dz ƏR ƏR dy' dz provided that certain "nice" conditions are met (which we assume). Let F(x, y, z) = (e² cos y, -e" sin y, 2). (c) Evaluate the integral F • dr, where C is the curve extending from the point (In 2, 7/2, 1) to (–1, , 0).
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