f(x):=

g(y):=

rot_x(f_):=[s,f(s)*COS(t),f(s)*SIN(t)]

rot_y(g_):=[g(s)*COS(t),g(s)*SIN(t),s]

v_x(f_,a,b):=pi*INT(f_^2,x,a,b)

v_y(g_,c,d):=pi*INT(g_^2,y,c,d)

lin(x1,y1,x2,y2,x):=(y1-y2)/(x1-x2)*(x-x1)+y1

fm(mat,x):=SUM(CHI(mat SUB i SUB 1,x,mat SUB (i+1) SUB 1)*lin(mat SUB i SUB 1~
,mat SUB i SUB 2,mat SUB (i+1) SUB 1,mat SUB (i+1) SUB 2,x),i,1,DIM(mat)-1)