/sci/ - Science & Math

penis

>there are brainlets on /sci/ who would write [math] \int f(x)\mathrm{d}x [/math] instead of [math] \int f(x)\, \mathrm{d}x [/math].

>>8921599
but is is a constant

>>8921609
Not quite. It's a free variable.

>>8921609
then what is its value?

check mate

>>8921617
any real number

>>8921614
wrong

if it was anything other than constant then the right hand side wouldn't derive to be f(x)

>ThErE aRe BrAiNlEtS oN /sCi/ WhO tHiNk C iN ∫f(X)dX=f(X)+c Is A cOnStAnT

>>8921625
>if it was anything other than constant then the right hand side wouldn't derive to be f(x)
Are you sure you understand what a free variable is?

>>8921632
>Are you sure you understand what a free variable is?
yes

>>8921625
>any real number
>constant
pick one

>>8921625
you can take the derivative with respect to c

>>8921639
which real number isn't constant?

It is though, constant refers to the type of function it is

>>8921646
So basically it should be written as c(x), but since its value itself is constant, the argument is left out

it's a constant in each solution of the set of solutions to the integral

>>8921651
but it doesn't have to assume the same value on the whole domain, it the domain is for example sum of disjoint intervals then c, or c(x) has to be constant on each of the intervals but may assume different values on different intervals, so it doesn't have to be constant but just locally constant.

>>8921676
>, it the domain is for example sum of disjoint intervals then c
then it's not differentiable

>>8921691
so tan x or 1/x^2 are not integrable?

>>8921702
>tan x
That is not integratable on R.

>>8921702
not on [math] \mathbb{R} [/math]

>>8921716
>>8921718
They are integrable on their domains, it's meaningless to talk about integral of function in points where it doesn't exist

>>8921765
i've always seen integrability defined in terms of a single closed interval, what definition are you using?

>>8921765
>They are integrable on their domains
If you look at tan:R -> R it is NOT integratable, by the only definition of integratability (the integral over the set according to the measure is finite) I have ever heard of.

>>8921779
tan:R -> R it is NOT a function

It's constant versus the variable of integration
Nobody in this thread got to ode apparently

>>8921854
Yes, just take tan:R -> R*, or ignore the infinities, they are irrelevant anyways for considering the integral.