A) Use Green's theorem to compute the area inside the x2 y² ellipse + 19² 14² Use the fact that the area can be written as Hint: ä(t) The area is - 1₂ dx dy = 1/2 Lo D ƏD = 1. 19 cos(t). −y dx + x dy .

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A)
Use Green's theorem to compute the area inside the
x² y²
ellipse +
19² 14²
Use the fact that the area can be written as
11₂ dx dy
-
=
: 1.
Hint: x(t) = 19 cos(t).
The area is
1
SOD
OD
2
−y dx + x dy .
B)
Find a parametrization of the curve 2/3 + y2/3 = 92/3
and use it to compute the area of the interior.
Hint: x(t) = 9 cos³(t).
Transcribed Image Text:A) Use Green's theorem to compute the area inside the x² y² ellipse + 19² 14² Use the fact that the area can be written as 11₂ dx dy - = : 1. Hint: x(t) = 19 cos(t). The area is 1 SOD OD 2 −y dx + x dy . B) Find a parametrization of the curve 2/3 + y2/3 = 92/3 and use it to compute the area of the interior. Hint: x(t) = 9 cos³(t).
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