Consider the vector field F(x, y) = (3y² – 2xy, 6ry – x²). (a) Show that F is conservative. (b) Find the amount of work done by F in moving an object along the curve given by Ř(t) = (ť² sin(rt) , (t + 1)² + 2t cos(nt)+2t ) from t = 0 to %3D 1+ VE t = 1.

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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Consider the vector field F(x, y) = (3y² – 2xy, 6xy – x?).
(a) Show that F is conservative.
(b) Find the amount of work done by F in moving an object along the curve
given by R(t)
sin(rt)
1+ yi'
(t + 1)2 + 2t cos(at) + 2t ) from t = 0 to
t = 1.
Transcribed Image Text:Consider the vector field F(x, y) = (3y² – 2xy, 6xy – x?). (a) Show that F is conservative. (b) Find the amount of work done by F in moving an object along the curve given by R(t) sin(rt) 1+ yi' (t + 1)2 + 2t cos(at) + 2t ) from t = 0 to t = 1.
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