For part ii$,$ assume that n $=5$steps $3-$ A force required to hold a spring that has been stretched given by $\backslash ($ y$=$e$^\{$F $\backslash$times $2\backslash$times $10^\{-3\}\}\backslash ).$

a$)$ How much work is done in stretching the spring if the force increases from $100$ N to $500$ N using:

i$)$ An analytical integration technique

ii$)$ A numerical integration technique assume $\backslash (\backslash$mathbf$\{$n $=5$ s t e p s$\}\backslash )$

$[$Note: the work done is given by the area under the curve$]$

b$)$ Compare the two answers.

c$)$ Using a computer spreadsheet increases the number of values used for your numerical method.

d$)$ Analyse any effect the size of numerical step has on the result.