You can pass the limits to integrate directly:
>>> integrate(1/(x**2+y**2)**Rational(3,2), (y, -L/2, L/2))
L/(x**3*sqrt(L**2/(4*x**2) + 1))
It's generally recommended to do this as it isn't always correct to
substitute the upper and lower values directly. However, this result
is equivalent to yours in this case, after pulling a 4 out of the
square root.
Aaron Meurer
On Fri, Oct 19, 2018 at 10:17 AM bb <
burakb...@gmail.com> wrote:
>
> A physics teacher on an online course [presented][1] this integral,
>
> $$
> = \frac{1}{4\pi\epsilon_0} \frac{Q x}{L}
> \int _{-L/2}^{L/2} \left(\frac{dy}{(x^2+y^2)^{3/2}} \right) \hat{x}
> $$
>
> and said she solved it with Wolfram Alpha, which gave
>
> $$
> = \frac{1}{4\pi\epsilon_0} \frac{Q}{x \sqrt{x^2 + (L/2)^2}}\hat{x}
> $$
>
> I was wondering how to solve this using any other symbolic software like Sympy. I tried this for the indefinite integral,
>
> 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. Does anyone have any experience solving integrals such as the one above using symbolic software?
>
> [1]:
https://youtu.be/pJwg2Bk0BDE?t=1286
>
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