Suppose F(x, y) = (2y, – sin(y)) and C is the circle of radius 7 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation 7(t) for the circle C that starts at the point (7, 0) and travels around the circle once counterclockwise for 0

Suppose F(x, y) = (2y, – sin(y)) and C is the circle of radius 7 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation 7(t) for the circle C that starts at the point (7, 0) and travels around the circle once counterclockwise for 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Question

Suppose F(x, y) = (2y, – sin(y)) and C is the circle of radius 7 centered at the origin oriented counterclockwise.
(a) Find a vector parametric equation 7(t) for the circle C that starts at the point (7, 0) and travels around the circle once counterclockwise for 0 <t < 27.
T(t) =
(b) Using your parametrization in part (a), set up an integral for calculating the circulation of F around C.
F. dr =
- [ F(F(t)) - 7'(t) dt =
dt
with limits of integration a =
and b
(C) Find the circulation of F around C.
Circulation =

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