The derivative should actually be squared in the square root expression: sqrt(1 + f'(x)^2) (see e.g. https://en.wikipedia.org/wiki/Surface_of_revolution), which then simplifies to a rational function (x^6 + 1)/(2*x^3) (unless I made a mistake). Hence the integrand will be rational and SymPy should be able to handle it.
In general, the square root does simplify. In that case the result will be a hyperelliptic integral, which is non-elementary and cannot be represented by means of common special functions. There is no support in SymPy for such integrals. Kalevi Suominen On Saturday, January 21, 2023 at 4:32:16 PM UTC+2 Oscar wrote: > On Sunday, 15 January 2023 at 07:36:14 UTC zaqhie...@gmail.com wrote: > Hi all, > > I have a question: why SymPy (in JULIA and PYthon) unable to get the > numerical answer for area of surface of revolution? > > Is it impossible? > > This is my question posted today on Julia Discourse: > > > https://discourse.julialang.org/t/area-of-surface-of-revolution-integral-too-hard-to-be-computed-by-julia-sympy-and-python-sympy/92981 > > Please ask questions here rather than posting a link to somewhere else. > > You can numerically evaluate integrals using evalf: > > In [*1*]: x = symbols("x") > > ...: > > ...: f = (x**6 + 2)/(8*x**2) > > ...: g = sqrt(1 + diff(f,x)) > > ...: > > ...: h = 2*pi*Integral(((x**6 + 2)/(8*x**2))*sqrt(1 + diff(f,x)), (x, > 1, 3)) > > > In [*2*]: h > > Out[*2*]: > > 3 > > ⌠ > > ⎮ ___________________ > > ⎮ ╱ 3 6 > > ⎮ ⎛ 6 ⎞ ╱ 3⋅x x + 2 > > ⎮ ⎝x + 2⎠⋅ ╱ ──── + 1 - ────── > > ⎮ ╱ 4 3 > > ⎮ ╲╱ 4⋅x > > 2⋅π⋅⎮ ────────────────────────────────── dx > > ⎮ 2 > > ⎮ 8⋅x > > ⌡ > > 1 > > > In [*3*]: h.evalf() > Out[*3*]: 116.281297293490 > > > > -- > Oscar > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/67bcfe68-0057-453d-9b70-ec34028a0432n%40googlegroups.com.
