$\%$ SIMPSON'S COMPOSITE ALGORITHM $4\mathrm{.}1$

$\%$

$\%$ To approximate I $=$ integral $(($ f$($x$)$ dx $))$ from a to b:

$\%$

$\%$ INPUT: endpoints a$,$ b; even positive integer n$.$

$\%$

$\%$ OUTPUT: approximation XI to I.

syms$($OK$,$A$,$B$,$N$,$H$,$XI$0,$XI$1,$XI$2,$NN$,$I,X$,$XI$,$s$,$x$)$;

TRUE $=1$;

FALSE $=0$;

fprintf$(1,$'This is Simpsons Method.

$\text{'})$;

fprintf$(1,$'Input the function F$($x$)$ in terms of x

$\text{'})$;

fprintf$(1,$'For example: cos$($x$)$

$\text{'})$;

s $=$ input$(\text{'}\text{'},\text{'}$s$\text{'})$;

F $=$ inline$($s$,$x$)$;

OK $=$ FALSE;

while OK $==$ FALSE

fprintf$(1,$'Input lower limit of integration and $\text{'})$;

fprintf$(1,$'upper limit of integration

$\text{'})$;

fprintf$(1,\text{'}$on separate lines

$\text{'})$;

A $=$ input$(\text{'}\text{'})$;

B $=$ input$(\text{'}\text{'})$;

if A $>$ B

fprintf$(1,$'Lower limit must be less than upper limit

$\text{'})$;

else

OK $=$ TRUE;

end

end

OK $=$ FALSE;

while OK $==$ FALSE

fprintf$(1,$'Input an even positive integer N$.$

$\text{'})$;

N $=$ input$(\text{'}\text{'})$;

if N $>0$ && rem$($N$,2)==0$

OK $=$ TRUE;

else

fprintf$(1,$'Input must be even and positive

$\text{'})$;

end

end

if OK $==$ TRUE

$\%$ STEP $1$

H $=($B$-$A$)/$N;

$\%$ STEP $2$

XI$0=$ F$($A$)+$ F$($B$)$;

$\%$ summation of f$($x$(2*$I$-1))$

XI$1=0\mathrm{.}0$;

$\%$ summation of f$($x$(2*$I$))$

XI$2=0\mathrm{.}0$;

$\%$ STEP $3$

NN $=$ N $-1$;

for I $=1$:NN

$\%$ STEP $4$

X $=$ A $+$ I $*$ H;

$\%$ STEP $5$

if rem$($I$,2)==0$

XI$2=$ XI$2+$ F$($X$)$;

else

XI$1=$ XI$1+$ F$($X$)$;

end

end

$\%$ STEP $6$

XI $=($XI$0+2\mathrm{.}0*$ XI$2+4\mathrm{.}0*$ XI$1)*$ H $/3\mathrm{.}0$;

$\%$ STEP $7$

fprintf$(1,\text{'}$

The integral of F from $\%12\mathrm{.}8$f to $\%12\mathrm{.}8$f is

$\text{'},$ A$,$ B$)$;

fprintf$(1,\text{'}\%12\mathrm{.}8$f

$\text{'},$ XI$)$;

end

Please input the correct info to compute the following:

Integral $1-->2$ of x ln$($x$)$ dx $,$ n $=4$