[SOLVED] residue theorem (definite real integrals)

Hi everyone,

I didn't know where I should post my question as I'm new here; I hope this is the right place. Anyway, my question is:

I need to show that the following integral:

$\displaystyle

\int_0^{\infty} {\cos(t^2)}. dt

$

is equal to = $\displaystyle \frac{\sqrt\pi}{2\sqrt2}$

we're also given (i.e. can use)

$\displaystyle

\int_0^{\infty} {\exp(-u^2)}. du = \frac{\sqrt\pi}{2}

$

What is the best contour?

I think the residue will be zero as the function is analytic everywhere but the problem is how to prove that the contours used tend to zero?