On Fri, 19 Oct 2018 at 17:17, bb <[email protected]> wrote:
>
> A physics teacher on an online course [presented][1] this integral,
I haven't looked at the video but...
> from sympy import integrate, sqrt, Symbol, pprint
> y = Symbol('y')
> x = Symbol('x')
> print (integrate('1/ ((x**2+y**2)**(3/2))',y))
>
> Result is
>
> y/(x**3*sqrt(1 + y**2/x**2))
>
> I plugged in the limits,
>
> from sympy import simplify
> L = Symbol('L')
> x = Symbol('x')
> simplify((L/2)/(x**3*sqrt(1 + (L/2)**2/x**2)) - \
> (-L/2)/(x**3*sqrt(1 + (-L/2)**2/x**2)))
>
> I get
>
> 2*L/(x**3*sqrt(L**2/x**2 + 4))
>
> which does not look right.
I think this is correct. It just looks a bit strange because sympy
hasn't written it in the form you would normally use. The normal way
to write the result of the integral would be
>>> res = y/ (x**2 * (x**2+y**2)**Rational(1/2))
>>> res
y/(x**2*sqrt(x**2 + y**2))
We can see that this also differentates back to what you started with:
>>> res.diff(y)
-y**2/(x**2*(x**2 + y**2)**(3/2)) + 1/(x**2*sqrt(x**2 + y**2))
>>> simplify(res.diff(y))
(x**2 + y**2)**(-3/2)
--
Oscar
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