restart;
f := x->x+sin(x);
f(3);
V := int(Pi*f(x)^2, x = 0 .. 4);
simplify(V);
V2 := Pi*((1/3)*4^3-(2*4)*cos(4)+2*sin(4)+2-(1/4)*sin(8));
A := V-V2;
simplify(A);
g := x->x/(1-x);
V3 := int(Pi*g(x)^2, x = 0 .. 1/2);