Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 1 / 16 / c

In the Gamma function integral at $p=1/2$, use $x=t^2$, $dx=2tdt$, with $t>0$. Then $x^{-1/2}dx=2dt$, soThe substitution can first be made on finite positive intervals and then extended by monotone limits, justifying the endpoint passage.