23.2 Problem. Clean this up using the following more general approach. Let h: R→ C be continuous and integrable and let a R\{0}. Prove that 1 [ h(ax) dx = |a| 8 h(u) du. What does this say about g(a.) for a 0 and |g| integrable? [Hint: write the integral as h(ax) dx = limR+∞ √ Rh(ax) dx. Change variables in the definite integral but pay attention to how the sign of a affects the limits of integration and then the limit in R.]
23.2 Problem. Clean this up using the following more general approach. Let h: R→ C be continuous and integrable and let a R\{0}. Prove that 1 [ h(ax) dx = |a| 8 h(u) du. What does this say about g(a.) for a 0 and |g| integrable? [Hint: write the integral as h(ax) dx = limR+∞ √ Rh(ax) dx. Change variables in the definite integral but pay attention to how the sign of a affects the limits of integration and then the limit in R.]
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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![23.2 Problem. Clean this up using the following more general approach. Let h: R→ C
be continuous and integrable and let a R\{0}. Prove that
1
[ h(ax) dx =
|a|
8
h(u) du.
What does this say about g(a.) for a 0 and |g| integrable? [Hint: write the integral as
h(ax) dx = limR+∞ √ Rh(ax) dx. Change variables in the definite integral but pay
attention to how the sign of a affects the limits of integration and then the limit in R.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F690bc708-737a-4036-8bde-cd8ee17ec8dd%2F6388ecce-bb8e-47fd-b2ff-67268933660f%2Ffqirf6c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:23.2 Problem. Clean this up using the following more general approach. Let h: R→ C
be continuous and integrable and let a R\{0}. Prove that
1
[ h(ax) dx =
|a|
8
h(u) du.
What does this say about g(a.) for a 0 and |g| integrable? [Hint: write the integral as
h(ax) dx = limR+∞ √ Rh(ax) dx. Change variables in the definite integral but pay
attention to how the sign of a affects the limits of integration and then the limit in R.]
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