$\%$Your task for this lab assignment is to correctly implement

$\%$the functions called by integration$1$:

$\%$ leftriemannsum, rightriemannsum, and midpointriemannsum

$\%$based on their comments, provided code, and examples.

$\%$The function integration$1$ assumes arg$1$ is a floating point number a$.$

$\%$The function integration$1$ assumes arg$2$ is a floating point number b$.$

$\%$The function integration$1$ assumes arg$3$ is an integer for n$.$

$\%$This function assumes a $<=$ b and n $>0.$

$\%$The function integration$1$ is already implemented for you to have

$\%$consistent I$/$O with our examples. After you finish implementing

$\%$the functions aforementioned, you should not change the source

$\%$code in integration$1.$

function $[]=$ integration$1($arg$1,$ arg$2,$ arg$3)$

a $=$ str$2$num$($arg$1)$;

b $=$ str$2$num$($arg$2)$;

n $=$ ceil$($str$2$num$($arg$3))$;

fprintf$("$Let f$($x$)=3*$e$^(-$x$^2).$

$")$;

fprintf$("$Approximating the integral of f$($x$)$ over the interval

$")$;

fprintf$("[\%\mathrm{.}8$f$,\%\mathrm{.}8$f$]$ for n $=\%$i$.$

$",$ a$,$ b$,$ n$)$;

approx $=$ leftriemannsum$($a$,$ b$,$ n$)$;

absError $=$ absoluteerror$($approx$,$ a$,$ b$)$;

fprintf$("$Left hand Riemann sum $=\%15\mathrm{.}8$f$,$ absolute error $=\%15\mathrm{.}8$f

$",$ approx, absError$)$;

approx $=$ rightriemannsum$($a$,$ b$,$ n$)$;

absError $=$ absoluteerror$($approx$,$ a$,$ b$)$;

fprintf$("$Right hand Riemann sum $=\%15\mathrm{.}8$f$,$ absolute error $=\%15\mathrm{.}8$f

$",$ approx, absError$)$;

approx $=$ midpointriemannsum$($a$,$ b$,$ n$)$;

absError $=$ absoluteerror$($approx$,$ a$,$ b$)$;

fprintf$("$Midpoint Riemann sum $=\%15\mathrm{.}8$f$,$ absolute error $=\%15\mathrm{.}8$f

$",$ approx, absError$)$;

end

$\%$Return sum, the left hand Riemann sum

$\%$of f$($x$)$ from a to b using n rectangles.

$\%$You should call f$($x$)$ to implement this function.

$\%$Do not use any built$-$in Matlab functions

$\%$to implement this function.

function $[$sum$]=$ leftriemannsum$($a$,$ b$,$ n$)$

end

$\%$Return sum, the right hand Riemann sum

$\%$of f$($x$)$ from a to b using n rectangles.

$\%$You should call f$($x$)$ to implement this function.

$\%$Do not use any built$-$in Matlab functions

$\%$to implement this function.

function $[$sum$]=$ rightriemannsum$($a$,$ b$,$ n$)$

end

$\%$Return sum, the midpoint Riemann sum

$\%$of f$($x$)$ from a to b using n rectangles.

$\%$You should call f$($x$)$ to implement this function.

$\%$Do not use any built$-$in Matlab functions

$\%$to implement this function.

function $[$sum$]=$ midpointriemannsum$($a$,$ b$,$ n$)$

end

$\%$Return y$,$ f evaluated at x$.$

$\%$Call this function to implement

$\%$the other functions above.

$\%$You should not change this function.

function $[$y$]=$ f$($x$)$

y $=3*$exp$(-$x$^2)$;

end

$\%$Return absError$,$ the absolute error between v and

$\%$the area under the curve for f$($x$)$ over $[$a$,$ b$].$

$\%$You should not change this function.

function $[$absError$]=$ absoluteerror$($v$,$ a$,$ b$)$

area $=-(3*$pi$^(1/2)*($erf$($a$)-$ erf$($b$)))/2$;

absError $=$ abs$($v $-$ area$)$;

end