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 - 1. Jf, dx dy = 1/2 Lo −y dx + x dy . Hint: x(t) = 19 cos (t). The area is 836 B) Find a parametrization of the curve 2/3 + y2/3 = 92/3 x and use it to compute the area of the interior. Hint: x(t) = 9 cos³(t).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.5: The Area Between Two Curves
Problem 28E
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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
= 1.
=
If, dx dy = 2/1/20 −y dx + x dy.
ƏD
Hint: x(t) = 19 cos(t).
The area is 836
B)
Find a parametrization of the curve 2/3 + y2/3
and use it to compute the area of the interior.
Hint: x(t) = 9 cos³ (t).
=
92/3
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 = 1. = If, dx dy = 2/1/20 −y dx + x dy. ƏD Hint: x(t) = 19 cos(t). The area is 836 B) Find a parametrization of the curve 2/3 + y2/3 and use it to compute the area of the interior. Hint: x(t) = 9 cos³ (t). = 92/3
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ISBN:
9780321964038
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GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,