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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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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.
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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