SymPy Simplify Took too Long for Area of Surface Revolution of a sphere

[j_verzani]

@Freya_the_Goddess

f(x) = sqrt(r^2 - x^2)
# simplify(diff(f(x),x))
# we cannot use diff inside the fd(x) since QuadGK can't comprehend diff
fd(x) = -x/(sqrt(r^2 - x^2))
g(x) = sqrt(1 + (fd(x))^2)

h(x) = f(x)*g(x)

To elaborate, it also really helps to call simplify prior to computing:

julia> @time ex = integrate(2PI*simplify(h(x)), (x, -r, r))
  0.043363 seconds (13.71 k allocations: 715.979 KiB, 9.07% compilation time)
     2
4⋅π⋅r