Okay, maybe I can accept this readily. Easy enough to prove that doubling the height of a convex 2-d shape will double the area if you stretch all of its vertic

Okay, maybe I can accept this readily. Easy enough to prove that doubling the height of a convex 2-d shape will double the area if you stretch all of its vertical proportions to double. If that shape is on a graph, the x axis is what it normally is, and the internal height of the shape for a given value of x is given by f(x), when you double the height it will be given by 2*f(x). The integral of a function times a constant is that constant times the integral of the function, so the area inside the shape would double. I don't remember multivariable at all, would someone be willing to offer a 3-d proof?