\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find the value of the definite integral \(\displaystyle \int_0^{\sqrt{\pi}} 2x\cos(x^2) \,dx\).
\(\displaystyle\int_0^{\sqrt{\pi}} 2x\cos(x^2)\;dx =\)