The function $A=(\sin(y)\sin(z)+\cos(y)\cos(z))\sin(w)\sin(x)+\cos(w)\cos(x)$, given $w\in[0,\pi], x\in[0,\pi], y\in[0,2\pi], z\in[0,2\pi]$, defines a three-dimensional "surface" in 4D. ($A = f(w,x,y,z)$ represent level sets). How would I calculate the hyper-area of this surface as a function of A?
thank you!
p.s. I don't necessarily need a closed-form solution, I'm going to evaluate the integral numerically, but I don't know what the integral should be.