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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.

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    Oh, $A$ is not a parametrization. I believe your equation involving $A$ is a level-set for a function of $4$ variables. Is $A$ supposed to describe the level set? i.e. you're solving for $x,y,z,w$ in terms of $A$? My initial answer was assuming you had a parametrization.2011-04-21
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    Yes, you are correct.2011-04-21

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