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## Main Question or Discussion Point

I've attached my work, but basically, I'm trying to compute this:

[tex]\int_{0}^{\infty}2\sin({x^2})dx[/tex].

(The 2 is only there because when you expand it into an exponential function, it makes like easier.)

You can look at my work to see what I did. My question now is, is it possible to express that limit in exact form? If so, what is it? Why does the limit have this value?

http://img358.imageshack.us/img358/7304/file0004ch0.jpg [Broken]

I also tried doing this with double integrals and polar coordinates to calculate the square of the integral but I ran into a problem deep into it of evaluating [itex]\sin{\infty}[/itex] and [itex]\cos{\infty}[/itex].

If you're curious why I care about this, it's because this integral is important in the diffraction of light. While only the approximate answer is important in physics, I'm just curious about the mathematics behind it.

Thanks in advanced.

[tex]\int_{0}^{\infty}2\sin({x^2})dx[/tex].

(The 2 is only there because when you expand it into an exponential function, it makes like easier.)

You can look at my work to see what I did. My question now is, is it possible to express that limit in exact form? If so, what is it? Why does the limit have this value?

http://img358.imageshack.us/img358/7304/file0004ch0.jpg [Broken]

I also tried doing this with double integrals and polar coordinates to calculate the square of the integral but I ran into a problem deep into it of evaluating [itex]\sin{\infty}[/itex] and [itex]\cos{\infty}[/itex].

If you're curious why I care about this, it's because this integral is important in the diffraction of light. While only the approximate answer is important in physics, I'm just curious about the mathematics behind it.

Thanks in advanced.

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