$(30$ Points$)$ Numerically evaluate the integral

$\backslash$int$\_0^4[3+$x$*$cos$((\backslash$pi x$)/(4))]$dx

Using

$3-$point Newton$-$Cotes $($NC$)$ quadrature $(10$ points$).$

$2-$point Gauss$-$Legendre $($GL$)$ quadrature $(10$ points$).$

Which solution do you suppose would give more accurate results? Please justify your

answer $(10$ points$).$ Clearly explain why one method is better than another for a full

credit.

Please don't use AI$.$ It gets it wrong almost every time. Do the work yourself, show the work, and make sure it's correct. Only then will thumbs up$.$ Thank you.