Let I = ff, (a2 – y?) dæ dy, where D = {(a, v) : 1< *y < 4,0 < a – y < 6, # 2 0, y 2 0} Show that the mapping u = *y, v = * – y maps D to the rectangle R = [1, 4] × (0, 6]. (a) Compute 8 (a, v)/(u, v) by first cornputing 8 (u, v)/8(*, 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. (a) %3D (b)I = %3D
Let I = ff, (a2 – y?) dæ dy, where D = {(a, v) : 1< *y < 4,0 < a – y < 6, # 2 0, y 2 0} Show that the mapping u = *y, v = * – y maps D to the rectangle R = [1, 4] × (0, 6]. (a) Compute 8 (a, v)/(u, v) by first cornputing 8 (u, v)/8(*, 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. (a) %3D (b)I = %3D
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 = ff, (a2 – 2) da dy, where
D = {(*, 3) : 1< *y < 4,0 < a – y < 6, a > 0, y 2 0}
Show that the mapping u = sy, v = * – y maps D to the rectangle R = [1, 4] x (0, 6].
(a) Compute 8 (*, v)/8(u,v) by first computing 8 (u, v)/a(*, 3).
= v over R and evaluate.
(b) Use the Change of Variables Formula to show that I is equal to the integral of f (u, v):
(a) a(4)
=
(b)I :](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d542e43-f72e-4c8d-bde6-d6d94f4c4800%2F5094aefd-4daf-4dec-9f0b-25be933cc8c6%2Frlodwzm_processed.png&w=3840&q=75)
Transcribed Image Text:Let I = ff, (a2 – 2) da dy, where
D = {(*, 3) : 1< *y < 4,0 < a – y < 6, a > 0, y 2 0}
Show that the mapping u = sy, v = * – y maps D to the rectangle R = [1, 4] x (0, 6].
(a) Compute 8 (*, v)/8(u,v) by first computing 8 (u, v)/a(*, 3).
= v over R and evaluate.
(b) Use the Change of Variables Formula to show that I is equal to the integral of f (u, v):
(a) a(4)
=
(b)I :
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