Question Number 226777 by Spillover last updated on 14/Dec/25
$${Show}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}=\frac{\mathrm{4}−\pi}{\mathrm{4}} \\ $$$${Hence}\:{by}\:{using}\:{Simpson}^{'} {s} \\ $$$${rule}\:{find}\:{the}\:{value}\:\:{of}\:\pi \\ $$$${correct}\:{to}\:\mathrm{4}\:{decimal}\:{places} \\ $$