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

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