integrate( lambda(y),x^2+y^2))   could be mechanically converted to

integrate(x^2+y^2,  y)

 and vice versa.

There is a name for this in lambda calculus.  alpha conversion or some such 
thing.

Should you do this?
doesn't matter.  But if so, do it for summation, products, plotting,  etc.


On Saturday, April 9, 2016 at 5:38:33 PM UTC-7, Nils Bruin wrote:
>
> On Saturday, April 9, 2016 at 9:17:27 AM UTC-7, David Roe wrote:
>>
>>
>> Is there any ambiguity?  g is a function of one variable and we're 
>> specifying the variable of integration.  Is there a reason that we 
>> shouldn't allow indefinite_integral(g, x) to work?
>> David
>>
>> In you just use integral, this already does work. And it does NOT work by 
> using the specified variable as argument to a single variable function:
>
> sage: f(x)=x^2+y^2
> sage: integral(f,x)
> x |--> 1/3*x^3 + x*y^2
> sage: integral(f,y)
> x |--> x^2*y + 1/3*y^3
>
> I'm not sure that these semantics are particularly desirable, but they do 
> preclude assigning any other meaning to idefinite_integral(g,x).
>

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