Let D be the region enclosed by the ellipse 4 y? 1 9. above the x-axis. 1. Calculate the Jacobian using the change of variables 2u, and y = 3v. X = a(x, y) J(u, v) = a(u, v) 2. Rewrite the integral using the change of variables: y dA = = || f(u, v) du dv D S Determine f(u, v) and the region S. f(u, v) = S =||
Let D be the region enclosed by the ellipse 4 y? 1 9. above the x-axis. 1. Calculate the Jacobian using the change of variables 2u, and y = 3v. X = a(x, y) J(u, v) = a(u, v) 2. Rewrite the integral using the change of variables: y dA = = || f(u, v) du dv D S Determine f(u, v) and the region S. f(u, v) = S =||
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:x2
y?
Let D be the region enclosed by the ellipse
4
9.
above the x-axis.
1. Calculate the Jacobian using the change of variables
2u, and y = 3v.
a(x, y)
a(u, v)
J(u, v)
2. Rewrite the integral using the change of variables:
y dA = ||
/| f(u, v) du dv
D
S
Determine f(u, v) and the region S.
f(u, v) = |
s-
S =||
a {(и, 0) | и? + v? <1}
b { (и, v) | u? + v? < 1, и > 0}
c { {u, v) | u² + v² < 1, v > 0 }
d { (u, v) | u² + v² < 1, u > 0, v > 0 }
e { (u, v) | u² + v² = 1 }
||
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