Compute the following 3 integrals: e¬l=le-ikz, dr dr 2 1 (1+. Yes, that's an absolute value in the exponent. Yes, one of those integrals is just a Fourier transform. Yes, one of those integrals is remarkably simple to calculate, even with the square. Yes, one of those integrals is really difficult if you don't remember an important property of Fourier transforms, and it's remarkably easy if you do remember that property of Fourier transforms.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Compute the following 3 integrals:
dx
2n
dr
2
1
5dr
(1 + x²)2 dx
Yes, that's an absolute value in the exponent. Yes, one of those integrals is just a Fourier transform.
Yes, one of those integrals is remarkably simple to calculate, even with the square. Yes, one of those
integrals is really difficult if you don't remember an important property of Fourier transforms, and
it's remarkably easy if you do remember that property of Fourier transforms.
Transcribed Image Text:Compute the following 3 integrals: dx 2n dr 2 1 5dr (1 + x²)2 dx Yes, that's an absolute value in the exponent. Yes, one of those integrals is just a Fourier transform. Yes, one of those integrals is remarkably simple to calculate, even with the square. Yes, one of those integrals is really difficult if you don't remember an important property of Fourier transforms, and it's remarkably easy if you do remember that property of Fourier transforms.
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