beginfig(2);
u := 1cm;

path p;

% Koordinatensystem
z0=(0,0);  z1=(5u,-u);  z2=(3u,2u);
drawarrow z0--(0,4u);
drawarrow z0--z1;  drawarrow z0--z2;

% die Gebietsprojektion
p = (2.4u,0.4u){0,-1}..(3.3u,0.4u)..(4.6u,0.3u)..{0,1}(5.9u,0.5u){0,1}..
  (3.8u,1.2u)..cycle;
fill p withcolor 0.9white; draw p;
drawarrow (6u,0.2u)--(5u,0.5u);
label.lrt(btex $B$ etex,(6u,0.2u));

% der Erdapfel
draw (2.4u,3u)..(4.5u,2.7u)..(5.9u,3.4u)..(4.5u,4.6u)..
  (3.8u,4.3u)..(3.2u,4.1u)..cycle;
drawarrow (3u,5u)--(4u,4u);
label.ulft(btex $V$ etex,(3u,5u));

% finde nun y-achsenparalle Linien
whatever[z2,z0] + m[z1,z0] = (2.4u,.4u);
whatever[z2,z0] + o[z1,z0] = (5.9u,.3u);
draw (2.4u,3u)--(2.4u,.4u)--(m[z1,z0]) dashed evenly;
draw (5.9u,3.4u)--(5.9u,0.3u)--(o[z1,z0]) dashed evenly;
label.llft(btex $x_u$ etex,m[z1,z0]);
label.llft(btex $x_o$ etex,o[z1,z0]);
label.bot(btex $f(x)$ etex,(4u,0.3u));
label.top(btex $g(x)$ etex,(4.3u,1.3u));
endfig;

end;