To evaluate the following integral, carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. c. Compute the Jacobian. d. Change variables and evaluate the new integral. Sxy da v R where R is the square with vertices (0,0), (3,3), (6,0), and (3,-3); use x=3u+3v, y=3u-3v. b. Find the limits of integration. 0 sus 1 0 svs 1 (Simplify your answers.) c. J(u,v) = (Simplify your answer.) ww √i S Hi C (0,0)
To evaluate the following integral, carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. c. Compute the Jacobian. d. Change variables and evaluate the new integral. Sxy da v R where R is the square with vertices (0,0), (3,3), (6,0), and (3,-3); use x=3u+3v, y=3u-3v. b. Find the limits of integration. 0 sus 1 0 svs 1 (Simplify your answers.) c. J(u,v) = (Simplify your answer.) ww √i S Hi C (0,0)
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:To evaluate the following integral, carry out these steps.
a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables.
b. Find the limits of integration for the new integral with respect to u and v.
c. Compute the Jacobian.
d. Change variables and evaluate the new integral.
Sxy dav
dA, where R is the square with vertices (0,0), (3,3), (6,0), and (3,-3); use x=3u +3v, y=3u-3v.
R
b. Find the limits of integration.
0 sus 1
0 svs
(Simplify your answers.)
c. J(u,v) = (Simplify your answer.)
-
GOOD
√i Vi
(0,0)
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