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How to calculate improper integral $\int_{0}^{\pi}{\frac{\sin{t}}{\sqrt{t}}dt}$?

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closed as off-topic by Ricardo Andrade, Lucia, Felipe Voloch, Nate Eldredge, Dylan Thurston Jun 8 '14 at 15:45

This question appears to be off-topic. The users who voted to close gave these specific reasons:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Lucia, Dylan Thurston
  • "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – Ricardo Andrade, Felipe Voloch, Nate Eldredge
If this question can be reworded to fit the rules in the help center, please edit the question.

This is more suitable on M.SE. – Sanath K. Devalapurkar Jun 8 '14 at 15:21
Maybe the rush to downvote and close (excuse me, put "on hold") was a bit hasty... This is not an elementary integral; I see that it can be evaluated in terms of the complex error function, but I doubt that it can be simplified further. – Noam D. Elkies Jun 8 '14 at 16:10
@NoamD.Elkies I agree that the downvotes may have been hasty; I didn't downvote, but I easily could have. However questions like this about evaluating definite integrals seem to be more at home at math.SE (even quite difficult integrals, which often receive extremely impressive answers there!). So the best outcome may be for this question to be moved to math.SE. – Tom Church Jun 8 '14 at 16:13
Just asking WolframAlpha to compute it, turns up the link with Fresnel integrals. Is there more to be said? – Lucia Jun 8 '14 at 16:18
Meaning that Wolfram Alpha is capable of making the change of variable $x\mapsto x^2$ correctly. I can do that too, so I'm not impressed. "Is there more to be said?" is exactly the question asked by the OP. My guess is "No", but I have no proof that the answer is algebraicly independent with $e$ and $\pi$, so, if it is "not research level", it is not because it is below the current level of advanced research but because the current knowledge is severely insufficient to answer questions of this kind. If that is what was meant by those who voted to close, I agree. – fedja Jun 8 '14 at 17:56

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