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Member warned about not using the homework template

The question asks whether the following converges or diverges.

[tex]\int_{0}^{\infty } \frac{\left | sinx \right |}{x^2} dx[/tex]

Now I think there might be a trick with the domain of sine function but I couldn't make up my mind on this.

I tried to compare it with 1/x^2, (sinx)/x, and sinx. I actually expected that I would get something good with 1/x^2, but as the lower limit of the integral is zero, it ended up with infinity on (0, inf) and since 1/x^2 is greater than (sinx)/x^2, and is divergent as we just found, we cannot say whether the given function diverges or converges. So I'm wondering what is the right track on this question?

[tex]\int_{0}^{\infty } \frac{\left | sinx \right |}{x^2} dx[/tex]

Now I think there might be a trick with the domain of sine function but I couldn't make up my mind on this.

I tried to compare it with 1/x^2, (sinx)/x, and sinx. I actually expected that I would get something good with 1/x^2, but as the lower limit of the integral is zero, it ended up with infinity on (0, inf) and since 1/x^2 is greater than (sinx)/x^2, and is divergent as we just found, we cannot say whether the given function diverges or converges. So I'm wondering what is the right track on this question?

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