Problem: Numerical Integration

A cross$-$section of a sailboat is shown below, demonstrating how wind forces are exerted and vary as a function of distance above the deck, $h,$ from $0$ to $28$ feet.

Calculate the total force, F$,$ exerted on the boat by using a numerical integration approach of your choice to integrate the continuous function:

$F={\displaystyle \underset{0}{\overset{28}{}}}200(\frac{h}{5+h})e^{(-2\frac{h}{28})}dh$

A$.$ Report the total force, $F,$ for each step size of: $1\mathrm{.}0ft,0\mathrm{.}5ft,0\mathrm{.}1ft,0\mathrm{.}05ft,$ and $0\mathrm{.}01ft($in other words the area from $0$ to $28$ divided into $1ft$ segments, etc$)$

B$.$ Without any 'true' value to compare to$,$ how can you analyze your approximation error? Consider the results you have calculated in part A$,$ and provide a brief explanation $($additional calculations optional$)$