Suppose F(x, y) = (e², e³) and C' is the portion of the ellipse centered at the origin from the point (0, 1) to the point (7,0) centered at the origin oriented clockwise. (a) Find a vector parametric equation 7²(t) for the portion of the ellipse described above for 0 < t < π/2. r(t) = (b) Using your parametrization in part (a), set up an integral for calculating the circulation of around C. L.F. F.dr = = ["* F (F(t)) · F' (t) dt = [" with limits of integration a = 0 (c) Find the circulation of Faround C. Circulation = and b = pi/2 dt
Suppose F(x, y) = (e², e³) and C' is the portion of the ellipse centered at the origin from the point (0, 1) to the point (7,0) centered at the origin oriented clockwise. (a) Find a vector parametric equation 7²(t) for the portion of the ellipse described above for 0 < t < π/2. r(t) = (b) Using your parametrization in part (a), set up an integral for calculating the circulation of around C. L.F. F.dr = = ["* F (F(t)) · F' (t) dt = [" with limits of integration a = 0 (c) Find the circulation of Faround C. Circulation = and b = pi/2 dt
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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Transcribed Image Text:Suppose F(x, y) = (e, e) and C' is the portion of the ellipse centered at the origin from the point (0, 1) to the point (7,0) centered at the origin oriented
clockwise.
(a) Find a vector parametric equation (t) for the portion of the ellipse described above for 0 < t < π/2.
r(t) =
=
(b) Using your parametrization in part (a), set up an integral for calculating the circulation of Faround C.
L.F.
· [° F (F(1) · F² (1) dt = [
dr =
with limits of integration a = 0
(c) Find the circulation of Faround C.
Circulation =
and b =
pi/2
dt
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