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Suppose F(x, y) = (2y, — sin(y)) and C' is the circle of radius 5 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation (t) for the circle C' that starts at the point (5,0) and travels around the circle once counterclockwise for 0 < t ≤ 2T. r(t) =<5cos(t),5sin(t)> (b) Using your parametrization in part (a), set up an integral for calculating the circulation of around C. L.F. [° F (F(t)) · F² (1) dt = [ dr with limits of integration a = 0 (c) Find the circulation of Faround C. Circulation = and b = 2pi dt

Suppose F(x, y) = (2y, — sin(y)) and C' is the circle of radius 5 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation (t) for the circle C' that starts at the point (5,0) and travels around the circle once counterclockwise for 0 < t ≤ 2T. r(t) =<5cos(t),5sin(t)> (b) Using your parametrization in part (a), set up an integral for calculating the circulation of around C. L.F. [° F (F(t)) · F² (1) dt = [ dr with limits of integration a = 0 (c) Find the circulation of Faround C. Circulation = and b = 2pi dt

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose F(x, y) = (2y, - sin(y)) and C' is the circle of radius 5 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation (t) for the circle C' that starts at the point (5,0) and travels around the circle once counterclockwise for 0 < t < 2. r(t) = = <5cos(t),5sin(t)> (b) Using your parametrization in part (a), set up an integral for calculating the circulation of F around C. | F. dr = · [ * F (F(1)) · F² (1) dt = [" with limits of integration a = 0 (c) Find the circulation of F Circulation = around C. and b = 2pi dt
Transcribed Image Text:Suppose F(x, y) = (2y, - sin(y)) and C' is the circle of radius 5 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation (t) for the circle C' that starts at the point (5,0) and travels around the circle once counterclockwise for 0 < t < 2. r(t) = = <5cos(t),5sin(t)> (b) Using your parametrization in part (a), set up an integral for calculating the circulation of F around C. | F. dr = · [ * F (F(1)) · F² (1) dt = [" with limits of integration a = 0 (c) Find the circulation of F Circulation = around C. and b = 2pi dt
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