Let F = (2y + 2)i +4ryj + rk. (a) Show whether F is conservative. (b) Using the fundamental theorem of calculus for line integrals, prove that F- dr = -a along a curve C defined by a vector function r(t) = cos ti + sin tj + tk for 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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Please answer (a),(b) and c in the following image.

Let F = (2y? + 2)i + 4ryj + rk.
(a) Show whether F is conservative.
(b) Using the fundamental theorem of calculus for line integrals, prove that
F. dr = -x
along a curve C defined by a vector function r(t) = cos ti + sin tj + tk for
(c) Using the definition, show that the curve C in part (b) is not closed.
Transcribed Image Text:Let F = (2y? + 2)i + 4ryj + rk. (a) Show whether F is conservative. (b) Using the fundamental theorem of calculus for line integrals, prove that F. dr = -x along a curve C defined by a vector function r(t) = cos ti + sin tj + tk for (c) Using the definition, show that the curve C in part (b) is not closed.
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