# set terminal png transparent nocrop enhanced font arial 8 size 420,320 
# set output 'bivariat.2.png'
set samples 50, 50
set title "approximate the integral of functions" 0.000000,0.000000  font ""
f(x)=sin(x)
integral_f(x) = (x>0)?integral1a(x):-integral1b(x)
integral1a(x) = (x<=0)?0:(integral1a(x-delta)+delta*f(x))
integral1b(x) = (x>=0)?0:(integral1b(x+delta)+delta*f(x))
integral2_f(x,y) = (x<y)?integral2(x,y):-integral2(y,x)
integral2(x,y) = (x>y)?0:(integral2(x+delta,y)+delta*f(x))
delta = 0.2
plot [-5:5] f(x) title "f(x)=sin(x)", integral_f(x)