Please show all work.

A simple batch distillation separates $100$ moles of a $10$mol$\%$ methanol and $90$mol$\%$ water

feed. The final bottoms concentration is $1$mol$\%$ methanol. VLE data are available in Table

$2-7.P=1$atm

a$.$ Find $W_{\text{f}\text{i}\text{n}\text{a}\text{l}},D_{\text{t}\text{o}\text{t}\text{a}\text{l}},$ and $x_{D,\text{a}\text{v}\text{g}}$ using Simpson's rule.

b$.$ Find $W_{\text{f}\text{i}\text{n}\text{a}\text{l}},D_{\text{t}\text{o}\text{t}\text{a}\text{l}},$ and $x_{D,\text{a}\text{v}\text{g}}$ using the Gaussian quadrature formula. $($Ans$.x_{D,\text{a}\text{v}\text{g}}=0\mathrm{.}2483)$

c$.$ Explain why the area calculated by Simpson's rule is too high