Prove that: $\displaystyle \int_0^{\infty}\sin(x^2)\,dx = \sqrt{\frac{\pi}{8}}$

Further prove that: $\displaystyle \int_0^{\infty}\sin(x^2)\,dx = \int_0^{\infty}\cos(x^2)\,dx$

Help on either one would be much appreciated.

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- Apr 29th 2009, 10:46 PMredsoxfan325Improper Integral
Prove that: $\displaystyle \int_0^{\infty}\sin(x^2)\,dx = \sqrt{\frac{\pi}{8}}$

Further prove that: $\displaystyle \int_0^{\infty}\sin(x^2)\,dx = \int_0^{\infty}\cos(x^2)\,dx$

Help on either one would be much appreciated. - Apr 29th 2009, 11:46 PMOpalg
- Apr 30th 2009, 12:03 AMredsoxfan325
Oh, so I imagine this is tough to prove. This isn't a homework problem or anything; I just found it by accident while using Maple and was curious why it was true.