function Ltotal $=$ calclift$($fun$,$ n$,$ w$)$

$\%$ calclift: Approximates the total lift over the entire wingspan using Simpson's $1/3$ rule.

$\%$ Inputs:

$\%$ fun $-$ function handle to the lift distribution function

$\%$ n $-$ number of node points $($must be even$)$

$\%$ w $-$ wingspan of the aircraft

$\%$ Output:

$\%$ Ltotal $-$ total lift over the full span

$\%$ Ensure the number of nodes is even, as required by Simpson's rule

if mod$($n$,2)$ ~$=0$

error$(\text{'}$Number of node points must be even for Simpson'$\text{'}$s $1/3$ rule.$\text{'})$;

end

$\%$ Define the semi$-$span

semi$\_$span $=$ w $/2$;

$\%$ Generate the y values for the node points

y $=$ linspace$(0,$ semi$\_$span, n $+1)$; $\%$ n$+1$ points define n subintervals

$\%$ Evaluate the lift distribution function at the node points

L$\_$values $=$ fun$($y$)$;

$\%$ Apply Simpson's $1/3$ rule

h $=($semi$\_$span$)/$ n; $\%$ width of each subinterval

Q $=($h $/3)*($L$\_$values$(1)+4*$ sum$($L$\_$values$(2$:$2$:end$-1))+2*$ sum$($L$\_$values$(3$:$2$:end$-2))+$ L$\_$values$($end$))$;

$\%$ Calculate the total lift over the full span

Ltotal $=2*$ Q;

end