3. Let F = (2y² + z)i + 4.ryj + ak. (a) Show whether F is conservative. (b) Using the fundamental theorem of calculus for line integrals, prove that F . · dr = -n along a curve C defined by a vector function r(t) = cos ti + sin tj + tk for 0

3. Let F = (2y² + z)i + 4.ryj + ak. (a) Show whether F is conservative. (b) Using the fundamental theorem of calculus for line integrals, prove that F . · dr = -n along a curve C defined by a vector function r(t) = cos ti + sin tj + tk for 0

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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can i get help with this line integral vector calculus question

[3]
3. Let F = (2y? + 2)i + 4.xyj+ xk.
%3D
(a) Show whether F is conservative.
(b) Using the fundamental theorem of calculus for line integrals, prove that
F. dr = -n
along a curve C defined by a vector function r(t) = cos ti + sin tj + tk for

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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