The code I was provided seems to have a problem. The percentage relative error cannot be negative. The picture below is the result of me running the c$++$ code

I want to be provided with the correct code.

The c$++$ code I received:

$--------------------------------$

#include

#include

#include

using namespace std;

$//$ Function to be integrated

double f$($double x$)\{$

return $1\mathrm{.}6*$ x $*$ x $*$ exp$($x$)$;

$\}$

$//$ Simpson's $1/3$ rule

double simpsonsRule$($double a$,$ double b$,$ int n$)\{$

double h $=($b $-$ a$)/$ n;

double sum $=$ f$($a$)+$ f$($b$)$;

for $($int i $=1$; i $$ n; i $+=2)\{$

sum $+=4*$ f$($a $+$ i $*$ h$)$;

$\}$

for $($int i $=2$; i $$ n $-1$; i $+=2)\{$

sum $+=2*$ f$($a $+$ i $*$ h$)$;

$\}$

return $($h $/3)*$ sum;

$\}$

int main$()\{$

double trueValue $=(1\mathrm{.}36*$ exp$(1\mathrm{.}6))-2$;

vector h$\_$values $=\{0\mathrm{.}16,0\mathrm{.}08,0\mathrm{.}04,0\mathrm{.}02,0\mathrm{.}01\}$;

vector n$\_$values;

vector errors;

vector relative$\_$errors;

$//$ Calculating n values

for $($double h : h$\_$values$)\{$

n$\_$values.push$\_$back$($static$\_$cast$((1-0)/$ h$))$;

$\}$

$//$ Calculating integrals and errors

cout h$\backslash$tIntegral$\backslash$tRelative Error $(\%)$

$"$;

for $($int n : n$\_$values$)\{$

double integral $=$ simpsonsRule$(0,1,$ n$)$;

double error $=$ fabs$($integral $-$ trueValue$)$;

double relative$\_$error $=($error $/$ fabs$($trueValue$))*100$;

errors.push$\_$back$($error$)$;

relative$\_$errors.push$\_$back$($relative$\_$error$)$;

cout nt$"$ integral t$"$ relative$\_$error

$"$;

$\}$

$//$ Calculating rate of change of percentage relative error

cout

Rate of Change of Percentage Relative Error:

$"$;

for $($size$\_$t i $=1$; i $$ relative$\_$errors.size$()$; $++$i$)\{$

double rate $=($relative$\_$errors$[$i$]-$ relative$\_$errors$[$i $-1])/($h$\_$values$[$i$]-$ h$\_$values$[$i $-1])$;

cout $$ "From h $="$ h$\_$values$[$i to h $="$ h$\_$values$[$i: $"$ rate

$"$;

$\}$

return $0$;

$\}$

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