Let D be the region bounded by the line x + y = 1 and the curve cos² t F(t) = (si12 0 ≤t≤ T/2. (a) The region D is sketched for you, and the curved part of its boundary is parametrized above. Give a parametrization for the other part of the boundary. Y X (b) Let F(x, y) = (). Compute fF. dr for each of the two pieces comprising the boundary of D.
Let D be the region bounded by the line x + y = 1 and the curve cos² t F(t) = (si12 0 ≤t≤ T/2. (a) The region D is sketched for you, and the curved part of its boundary is parametrized above. Give a parametrization for the other part of the boundary. Y X (b) Let F(x, y) = (). Compute fF. dr for each of the two pieces comprising the boundary of D.
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:5. Let D be the region bounded by the line x + y = 1 and the curve
cos² t
(C124), 0≤t≤5/2.
sin ¹2
r(t):
=
(a) The region D is sketched for you, and the curved part of its
boundary is parametrized above. Give a parametrization for the
other part of the boundary.
Y
X
(b) Let F(x, y) = (). Compute fF. dr for each of the two pieces
comprising the boundary of D.
(c) Using Green's Theorem and your answer to part (b), find the
area of D.
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