/sci/ - Science & Math

[Anonymous No.6504327]

I just discovered this paradox/contradiction.

The area between the x axis and the curve ln x between zero and one has a different area depending on which way you integrate.

Kind of interesting this means that if you have a container of finite volume where each 2D cross section is the shape defined above it would take a finite amount of water to fill the container if its opening was on the x-axis, but would take an infinite amount of water to fill if its opening was on the y-axis.


Assuming there is gravity acting on the water.


My proof is in the picture.

[Anonymous No.6504348]

>>6504327
Uh, the integral of lnx is not 1/x

[Anonymous No.6504353]

LOL

[Anonymous No.6504357]

[Anonymous No.6504374]

<div class="math">\int\! \log x \, \mathrm{d}x = x\log x - x+C</div>

[Anonymous No.6504380]

>>6504327
>I just discovered this paradox/contradiction.
new uncharted waters in integration! amazing anon! somebody call the Fields committee.

[Anonymous No.6505830]

>>6504327
I know this is rather pointless, but if you are honest anon. Did you really think you found a paradox?

[Anonymous No.6505865]

>>6504327
>2D
So many logic problems there alread

[Anonymous No.6506018]

>>6504327
>proof is in the picture
proof-by-picture is valid only in Topology

[Anonymous No.6507827]

Even aside from all the other obviously stupid shit, what's with your notation?

[Anonymous No.6507833]

>>6504327
He thinks that <span class="math"> \int ln(x)dx=\frac{1}{x} [/spoiler]