Problem $3(20$ points, Core Course Outcomes $1,6,$ & $11)$

For the case described in problem $2$ with $=3,$ determine the deflection at the beam's end $y(L)$ such that the estimated relative error is less than $+-{10}^{-5},$ when successively reducing the truncation error of the integrations by doubling the number of intervals $N$ used, starting with $N=32.$

In addition to the calculated $y(L),$ give the number of intervals $N$ necessary and graph in $5$ separate plots $p(x),F(x),M(x),(x),$ and $y(x).$ Use the given content obscured functions from problem $2$ to determine $p(x)$ and $EI(x,)$ at any $x$ and $$ needed.

Required submission:

name of integration method used $($named in code is not sufficient$)$;

beam's deflection at its end, $y(L)$

number of intervals $N$ necessary;

$5$ separate graphs showing $p(x),F(x),M(x),(x),$ and $y(x)$ respectively;

printout of script and any additional functions not already submitted in prior homework.