55. (Separated variables over a rectangle) Let R be the rectan- gle a < x < b, c < y < d. Show that, if f is continuous on [a, b] and g is continuous on [c, d], then || f(x)g(y) dxdy R (17.3.3)
55. (Separated variables over a rectangle) Let R be the rectan- gle a < x < b, c < y < d. Show that, if f is continuous on [a, b] and g is continuous on [c, d], then || f(x)g(y) dxdy R (17.3.3)
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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Separated variables over a rectangle.
![55. (Separated variables over a rectangle) Let R be the rectan-
gle a <x < b, c < y < d. Show that, if f is continuous on
[a, b] and g is continuous on [c, d], then
|| f(x)g(y) dx dy
R
(17.3.3)
f(x) dx 8(9)dy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b9a2144-dfc4-40f3-97fb-de24320ca2ba%2F9401bf8d-c4dc-4ef4-8789-f469349d2059%2Fnq1aba_processed.png&w=3840&q=75)
Transcribed Image Text:55. (Separated variables over a rectangle) Let R be the rectan-
gle a <x < b, c < y < d. Show that, if f is continuous on
[a, b] and g is continuous on [c, d], then
|| f(x)g(y) dx dy
R
(17.3.3)
f(x) dx 8(9)dy
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