Given that f(z, y) = z (2y+4) +y(7z - 14) is a potential function for F = (2y+4+7y, 2z + Ta - 14). calculate the integral F. dr. where Cis the upper haif of the unit circle oriented counterclockwise with parameterization r(1) = (co(t), sin(). O 5 sE Enter an enact answer. Provide your answer below

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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Given that f(x, y) = x (2y + 4) + y (7x – 14) is a potential function for F = (2y +4+ 7y, 2x + 7x – 14), calculate
the integral
F. dr, where C is the upper half of the unit circle oriented counterclockwise with parameterization
r(t) = (cos(t), sin(t)), 0 < t < r.
Enter an exact answer.
Provide your answer below:
Sc F•dr:
Transcribed Image Text:Given that f(x, y) = x (2y + 4) + y (7x – 14) is a potential function for F = (2y +4+ 7y, 2x + 7x – 14), calculate the integral F. dr, where C is the upper half of the unit circle oriented counterclockwise with parameterization r(t) = (cos(t), sin(t)), 0 < t < r. Enter an exact answer. Provide your answer below: Sc F•dr:
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