# Improper Integral

• Apr 29th 2009, 10:46 PM
redsoxfan325
Improper Integral
Prove that: $\int_0^{\infty}\sin(x^2)\,dx = \sqrt{\frac{\pi}{8}}$

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

Help on either one would be much appreciated.
• Apr 29th 2009, 11:46 PM
Opalg
• Apr 30th 2009, 12:03 AM
redsoxfan325
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.