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I've been working on a problem which requires the numerical evaluation of an improper integral. I would like to transform the limits of integration on [tex][0,\infty)[/tex] to the bounded region [tex][a,b][/tex] by replacing the variable [tex]\omega[/tex] with another variable. Here is the integral:

[tex]

u(t,\tau)=\frac{1}{\pi}\int_{0}^{\infty}\! G(\omega)\, d\omega

[/tex]

[tex]

G(\omega)=4\sqrt{\pi}\frac{\omega^{2}}{\omega_{0}^ {3}}\mbox{exp}\left(-\frac{\omega^{2}}{\omega_{0}^{2}}\right)\mbox{cos \left(\omega t-\left(\frac{\omega}{\omega_{0}}\right)^{-\gamma}\omega\tau\right)\mbox{exp}\left(-\frac{1}{2Q}\left(\frac{\omega}{\omega_{0}}\right) ^{-\gamma}\omega t\right)}

[/tex]

How should I proceed? Is there a relevant reference which could point me in the proper direction?

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# Transforming limits of integration to a bounded region

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