# # f := (x,y) -> x^2-y; S := n -> sum( f(j/n,j/n)*sqrt(2)/n,j=1..n); S2:=S(2)=evalf(S(2));S10:=S(10)=evalf(S(10));S100:= S(100)=evalf(S(100)); Answer := Int('f',s) = limit(S(n),n=infinity); r := t -> x(t)*i + y(t)*j + z(t)*k; dt := (b-a)/n; S := n-> sum(f(r(a+j*dt))*'ds.j/dt'*dt,j=1..n); Line_int := Int(f,s) = Limit('S(n)',n=infinity); Line_int := Int(f('r(t)')*v(t),t=a..b); Answer := Int((t^2-t)*sqrt(2),t=0..1) = int((t^2-t)*sqrt(2),t=0..1);