> Phi:=(y-2+sqrt(3)*x)*(y-sqrt(3)*x)*y/2;

                                 1/2          1/2
                       (y - 2 + 3    x) (y - 3    x) y
                Phi := -------------------------------
                                      2

> M:=2*Int(Int(Phi,x=y/sqrt(3)..(2-y)/sqrt(3)),y=0..1)                  
>                                                      
> =2*int(int(Phi,x=y/sqrt(3)..(2-y)/sqrt(3)),y=0..1);

                          1/2
                 (2 - y) 3
                 ------------
            1         3
           /    /                       1/2          1/2
          |    |              (y - 2 + 3    x) (y - 3    x) y
  M := 2  |    |              ------------------------------- dx dy
          |    |                             2
         /    /
           0       1/2
                y 3
                ------
                  3

            1/2
           3
         = ----
            45

> 
> M:=4*Int(Int(Phi, y=0..sqrt(3)*x), x=0..1/sqrt(3))                    
>                                                        =4*int(int(Phi,
> y=0..sqrt(3)*x), x=0..1/sqrt(3));

             1/2
            3
            ----     1/2
             3      3    x
           /       /                 1/2          1/2
          |       |        (y - 2 + 3    x) (y - 3    x) y
  M := 4  |       |        ------------------------------- dy dx =
          |       |                       2
         /       /
           0       0

         1/2
        3
        ----
         45

