#include

#include

#include

double f$($double x$)$

$\{$

return sin$($x$)$;

$\}$

double Trap$($int n$,$ double a$,$ double b$,$ double h$)$

$\{$

double T$,$ x;

int i;

T $=($f$($a$)+$ f$($b$))/2\mathrm{.}0$;

for $($i $=1$; i $<=$ n $-1$; i$++)$

$\{$

x $=$ a $+$ i $*$ h;

T $+=$ f$($x$)$;

$\}$

T $=$ T $*$ h;

return T;

$\}$

int main$($int argc, char$*$ argv$[])\{$

int rank, S$,$ n;

double a$,$ b$,$ h$,$ local$\_$a$,$ local$\_$b$,$ local$\_$integral, integral;

int local$\_$n;

MPI$\_$Init$($NULL$,$ NULL$)$;

MPI$\_$Comm$\_$rank$($MPI$\_$COMM$\_$WORLD, &rank$)$;

MPI$\_$Comm$\_$size$($MPI$\_$COMM$\_$WORLD, &S$)$;

if $($rank $==0)\{$

printf$("$Enter a$,$ b$,$ and n:

$")$;

scanf$\_$s$("\%$lf $\%$lf $\%$d$",$ &a$,$ &b$,$ &n$)$;

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

$\}$

MPI$\_$Bcast$($&a$,1,$ MPI$\_$DOUBLE, $0,$ MPI$\_$COMM$\_$WORLD$)$;

MPI$\_$Bcast$($&b$,1,$ MPI$\_$DOUBLE, $0,$ MPI$\_$COMM$\_$WORLD$)$;

MPI$\_$Bcast$($&n$,1,$ MPI$\_$INT, $0,$ MPI$\_$COMM$\_$WORLD$)$;

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

$//$ Compute the interval for each process

local$\_$n $=$ n $/$ S;

local$\_$a $=$ a $+$ rank $*$ local$\_$n $*$ h;

local$\_$b $=$ local$\_$a $+$ local$\_$n $*$ h;

$//$ Compute the area under the curve using the trapezoidal

local$\_$integral $=$ Trap$($local$\_$a$,$ local$\_$b$,$ local$\_$n$,$ h$)$;

MPI$\_$Reduce$($&local$\_$integral, &integral, $1,$ MPI$\_$DOUBLE, MPI$\_$SUM, $0,$ MPI$\_$COMM$\_$WORLD$)$;

$//$ Process $0$

if $($rank $==0)\{$

printf$("$With n $=\%$d trapezoids, our estimate of the integral from $\%$f to $\%$f $=\%$f

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

$\}$

MPI$\_$Finalize$()$;

return $0$;

$\}$

I need help calculating these values in the code $($With explanation$)$:

$1-$ execution time,

$2-$speedup $=$ Tserial$/$Tparallel

$3-$efficiency $=$ speedup$/$#threads