Born_to_be_patient
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- Joined
- Apr 1, 2022
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I have a pretty hard problem. I have to prove the divergence of the integral:
[math]\int_{0}^{+\infty} \frac {\sin(1/x)}{(x-\cos(\pi/x))^2}dx[/math]The integrand has an infinite number of discontinuity points in any neighborhood of zero. It is also unbounded at zero. I have tried to use the Cauchy criterion for the convergence of the integral, comparison Theorems, tried to evaluate the integrand but didn't succeed. Replacement [math]1/x=t[/math] didn't work either.
[math]\int_{0}^{+\infty} \frac {\sin(1/x)}{(x-\cos(\pi/x))^2}dx[/math]The integrand has an infinite number of discontinuity points in any neighborhood of zero. It is also unbounded at zero. I have tried to use the Cauchy criterion for the convergence of the integral, comparison Theorems, tried to evaluate the integrand but didn't succeed. Replacement [math]1/x=t[/math] didn't work either.
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