Let I = f(x² - y²) dx dy, where D = {(x, y) : 3 ≤ xy ≤ 4,0 ≤ x - y ≤ 3, x ≥ 0, y ≥ 0} Show that the mapping u = xy, v = x - y maps D to the rectangle R = [3, 4] × [0,3]. (a) Compute (x, y)/(u, v) by first computing (u, v)/8(x, y). (b) Use the Change of Variables Formula to show that I is equal to the integral of f(u, v) = v over R and evaluate. 8(z,y) = (b)I =
Let I = f(x² - y²) dx dy, where D = {(x, y) : 3 ≤ xy ≤ 4,0 ≤ x - y ≤ 3, x ≥ 0, y ≥ 0} Show that the mapping u = xy, v = x - y maps D to the rectangle R = [3, 4] × [0,3]. (a) Compute (x, y)/(u, v) by first computing (u, v)/8(x, y). (b) Use the Change of Variables Formula to show that I is equal to the integral of f(u, v) = v over R and evaluate. 8(z,y) = (b)I =
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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![Let I = f(x² - y²) dx dy, where
D = {(x, y) : 3 ≤ xy ≤ 4,0 ≤ x - y ≤ 3, x ≥ 0, y ≥ 0}
Show that the mapping u = xy, v = x - y maps D to the rectangle R = [3, 4] × [0,3].
(a) Compute (x, y)/(u, v) by first computing (u, v)/8(x, y).
(b) Use the Change of Variables Formula to show that I is equal to the integral of f(u, v) = v over R and evaluate.
8(z,y) =
(b)I =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccfd696e-cada-4e3a-b17f-a66c9ee4b0eb%2Fd632645b-0cc6-461f-987c-7208b461c3b5%2F81udz7j_processed.png&w=3840&q=75)
Transcribed Image Text:Let I = f(x² - y²) dx dy, where
D = {(x, y) : 3 ≤ xy ≤ 4,0 ≤ x - y ≤ 3, x ≥ 0, y ≥ 0}
Show that the mapping u = xy, v = x - y maps D to the rectangle R = [3, 4] × [0,3].
(a) Compute (x, y)/(u, v) by first computing (u, v)/8(x, y).
(b) Use the Change of Variables Formula to show that I is equal to the integral of f(u, v) = v over R and evaluate.
8(z,y) =
(b)I =
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