Find the area of the surface given by the parametrization:
$\vec r(u,v)=((2+\cos(u))\cos(v),(2+\cos(u))\sin(v), \sin(u))$ while $0 \le u,v \le 2\pi$.
I have tried to solve this question using the given parametrization in the normal way by finding $\vec r_u \times \vec r_v$.
But things got really complicated with all the $\cos, \sin$ with two different parameters.
I was wondering if there's any cool tricks or other ways I couldn't see in order to solve this question.
Thanks in advance.
Note: Final answer is $8\pi^2$