Why sympy gives different/wrong answer when integrate fraction of power? - integration

Question

I am running a definite integral but the sympy gives me a different answer.
I don't know what went wrong?
Can anyone help? Thanks
The equation integrated by Wolfram, the result is as expected 1.097
import sympy as sp
y=sp.Symbol('y')
fy=(y-2.4)**2*sp.sqrt(y)*0.1875
print(sp.integrate(fy,(y,0,4)))
This is giving me 0.485255751108899

Answer 1

This looks like a bug to do with floats that can be problematic in integration:
In [15]: from sympy import *
In [16]: y = symbols('y')
In [17]: fy=(y-2.4)**2*sp.sqrt(y)*0.1875
In [18]: fy
Out[18]:
2
1.08⋅√y⋅(0.416666666666667⋅y - 1)
In [19]: integ = Integral(fy, (y, 0, 4))
In [20]: integ
Out[20]:
4
⌠
⎮ 2
⎮ 1.08⋅√y⋅(0.416666666666667⋅y - 1) dy
⌡
0
In [21]: integ.doit() # symbolic integration with floats
Out[21]: 0.485255751108899
In [22]: integ.evalf() # numeric integration
Out[22]: 1.09714285714286
In [23]: integ_rational = Integral(nsimplify(fy), (y, 0, 4))
In [24]: integ_rational # same integral with Rational instead of Float
Out[24]:
4
⌠
⎮ 2
⎮ ⎛5⋅y ⎞
⎮ 27⋅√y⋅⎜─── - 1⎟
⎮ ⎝ 12 ⎠
⎮ ──────────────── dy
⎮ 25
⌡
0
In [25]: integ_rational.doit() # symbolic integration with rationals
Out[25]:
192
───
175
In [26]: _.n() # numerically evaluate the last result
Out[26]: 1.09714285714286
Firstly don't use floats with sympy unless you have a good reason e.g. use Rational('0.1') or S(1)/10 etc rather than 0.1. The nsimplify function can be used to convert float to Rational (it tries to guess what rational you really meant).
Secondly this is a bug so it should be reported to github rather than SO:
https://github.com/sympy/sympy/issues