Total marks 10 Total marks on naner: 80 7. Let DCR2 be a bounded domain with the boundary OD which can be represented as a smooth closed curve : [a, b] R2, oriented in the anticlock- wise direction. Use Green's Theorem to justify that the area of the domain D can be computed by the formula 1 Area(D) = ½ (−y, x) · dy. [5 Marks] (ii) Use the area formula in (i) to find the area of the domain D enclosed by the ellipse y(t) = (10 cos(t), 5 sin(t)), t = [0,2π]. [5 Marks]
Total marks 10 Total marks on naner: 80 7. Let DCR2 be a bounded domain with the boundary OD which can be represented as a smooth closed curve : [a, b] R2, oriented in the anticlock- wise direction. Use Green's Theorem to justify that the area of the domain D can be computed by the formula 1 Area(D) = ½ (−y, x) · dy. [5 Marks] (ii) Use the area formula in (i) to find the area of the domain D enclosed by the ellipse y(t) = (10 cos(t), 5 sin(t)), t = [0,2π]. [5 Marks]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 35RE
Related questions
Question
![Total marks 10
Total marks
on
naner: 80
7.
Let DCR2 be a bounded domain with the boundary OD which can be
represented as a smooth closed curve : [a, b] R2, oriented in the anticlock-
wise direction.
Use Green's Theorem to justify that the area of the domain D
can be computed by the formula
1
Area(D)
=
½ (−y, x) · dy.
[5 Marks]
(ii) Use the area formula in (i) to find the area of the domain D
enclosed by the ellipse
y(t) = (10 cos(t), 5 sin(t)),
t = [0,2π].
[5 Marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd66c7573-6777-48ff-9bfb-9b3df1a769a6%2F9571e69b-d38e-4455-bf11-7faf8ff2ea02%2Fr3ko4c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Total marks 10
Total marks
on
naner: 80
7.
Let DCR2 be a bounded domain with the boundary OD which can be
represented as a smooth closed curve : [a, b] R2, oriented in the anticlock-
wise direction.
Use Green's Theorem to justify that the area of the domain D
can be computed by the formula
1
Area(D)
=
½ (−y, x) · dy.
[5 Marks]
(ii) Use the area formula in (i) to find the area of the domain D
enclosed by the ellipse
y(t) = (10 cos(t), 5 sin(t)),
t = [0,2π].
[5 Marks]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 5 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,