# set terminal pngcairo transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 # set output 'bivariat.1.png' set key fixed right bottom vertical Right noreverse enhanced autotitle nobox set samples 50, 50 set style data lines set title "approximate the integral of functions" set xrange [ * : * ] noreverse writeback set x2range [ * : * ] noreverse writeback set yrange [ * : * ] noreverse writeback set y2range [ * : * ] noreverse writeback set zrange [ * : * ] noreverse writeback set cbrange [ * : * ] noreverse writeback set rrange [ * : * ] noreverse writeback set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front noinvert bdefault integral_f(x) = (x>0)?int1a(x,x/ceil(x/delta)):-int1b(x,-x/ceil(-x/delta)) int1a(x,d) = (x<=d*.1) ? 0 : (int1a(x-d,d)+(f(x-d)+4*f(x-d*.5)+f(x))*d/6.) int1b(x,d) = (x>=-d*.1) ? 0 : (int1b(x+d,d)+(f(x+d)+4*f(x+d*.5)+f(x))*d/6.) f(x) = exp(-x**2) integral2_f(x,y) = (xy-d*.5) ? 0 : (int2(x+d,y,d) + (f(x)+4*f(x+d*.5)+f(x+d))*d/6.) NO_ANIMATION = 1 delta = 0.2 plot [-5:5] f(x) title "f(x)=exp(-x**2)", 2/sqrt(pi)*integral_f(x) title "erf(x)=2/sqrt(pi)*integral_f(x)", erf(x) with points