4. . Consider the integral I = || ysin(zy) dA, R where Ris the shaded region shown on the diagram to the right. (a) Evaluate I. (b) Set r = u/v and y = v. Draw the image of Region R in the uv-plane. (c) Find the Jacobian of the transformation taking (x, y) to (u, v). (d) Evaluate the integral I by changing coordinates to (u, v).
4. . Consider the integral I = || ysin(zy) dA, R where Ris the shaded region shown on the diagram to the right. (a) Evaluate I. (b) Set r = u/v and y = v. Draw the image of Region R in the uv-plane. (c) Find the Jacobian of the transformation taking (x, y) to (u, v). (d) Evaluate the integral I by changing coordinates to (u, v).
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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Need help with part (d). Thank you :)
Transcribed Image Text:4. .
Consider the integral
I =
- || y sin(ry) dA,
R
xy=4
where Ris the shaded region shown on the diagram
to the right.
xy=1
(a) Evaluate I.
(b) Set z = u/v and y = v. Draw the image of Region R in the uv-plane.
(c) Find the Jacobian of the transformation taking (x, y) to (u, v).
(d) Evaluate the integral I by changing coordinates to (u, v).
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