/sci/ - Science & Math

[Anonymous No.11699494]

∫xdx on [−∞,∞] is equal to 0. If you disagree, you are objectively wrong and should fuck off.
>inb4 b-b-but if x=2+v then ∫(2+v)dv on [−∞,∞] so ur wrong
then you'd have to change the limits of integration and it would be different infinities so that's irrelevant retard, l2hyperreal
also, .9... is not equal to 1
pic related, it's a 1fag

[Anonymous No.11699512]

Every originally even function (with one side flipped) that is continuous and goes through origin will have integral from -inf to inf equal 0 and from -z to z equal 0 (where z is a real number)

[Anonymous No.11699519]

>>11699494
>>11699512
Moron.

[Anonymous No.11699522]

>>11699512
correct
>>11699519
fucktard

[Anonymous No.11699535]

>>11699494
take your meds

[Anonymous No.11699540]

>>11699535
>being this triggered by logic
>using a facebook-tier insult

[Anonymous No.11699544]

>>11699494
>used wrong notation for -infinity to +infinity
Stopped reading there

[Anonymous No.11699566]

>>11699544
>implying the integral should be the limit approaching infinity instead of the interval including infinity
kek at ur life kiddo

[Anonymous No.11699592]

>>11699494
>>11699512
this is how the integral IS defined: [math]\int_{-\infty}^{\infty}x \, dx = \lim_{a \to -\infty}\lim_{b \to \infty}\int_{a}^{b}x \, dx [/math]
this is how the interal IS NOT defined: [math]\int_{-\infty}^{\infty}x \, dx = \lim_{a \to \infty}\int_{-a}^{a}x \, dx [/math].
the integral doesn't exist and you're wrong.

[Anonymous No.11701289]

>>11699592
Doesn't change anything fucktard and regardless the integral is actually defined as the area between the curve and the x-axis, not as either of your dumb fuck nigger equations, if you have a problem take it up with Newton and Leibniz, I promise they would agree with me, the integral is 0 dumbfuck

[Anonymous No.11701309]

>>11699512
you mean odd? x is an odd function

[Anonymous No.11701311]

>>11701289
>Riemann integrals
>2020
yikes my dude

[Anonymous No.11701337]

>>11701309
You're right. I didn't know that "odd" means going through origin and symmetrical, but flipped. I thought it just means "not even".

[Anonymous No.11701357]

>>11699512
>>11699494
Why? Prove it.

[Anonymous No.11701390]

>>11699494
I'm mean you're not wrong. The regularized integral is indeed 0.
[math]\int_{-\infty}^\infty x dx = \int_{-\infty}^\infty \lim_{\varepsilon \rightarrow 0^+} x \exp(-x^2 \varepsilon) \overset{!}{=} \lim_{\varepsilon \rightarrow 0^+} \int_{-\infty}^\infty x \exp(-x^2 \varepsilon) = \lim_{\varepsilon \rightarrow 0^+} 0 = 0[/math]

[Anonymous No.11701398]

>>11699494
>>11701390
Nevermind, you are wrong about [math]0.\overline{9}[/math] not being equal to 1. It obviously is.

Let x = 0.999...
10x = 9.999...
9 + 0.999... = 9.999...
9 + x = 10x
10x - x = 9
9x = 9
x = 1

[Anonymous No.11702568]

>>11701311
>area under curve

[Anonymous No.11702740]

>>11701289
>the integral is actually defined as the area between the curve and the x-axis, not as either of your dumb fuck nigger equations
source: my ass