Ellipsoid surface function

Hello, I am trying to generate a function in order to calculate the total ellipsoid surface but I have a problem:

syms x y z p t;
elipsoide=[a*sin(p)*cos(t),b*sin(p)*sin(t),c*cos(p)];

ezsurf(elipsoide(1),elipsoide(2),elipsoide(3),[0,pi,0,2*pi])

rp=diff(elipsoide,p);
rt=diff(elipsoide,t);
n=cross(rp,rt);
aux=sqrt(n(1)^2+n(2)^2+n(3)^2);
auxsim=simplify(aux);

Then I need to integrate auxsim using numeric methods but I don't know how becaus auxsim is a symbolic function. Please I need your help.

Thanks!