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ISI UGB 2025 P1
SomeonecoolLovesMaths 4
N
by ZeroAlephZeta
Source: ISI UGB 2025 P1
Suppose 
is differentiable and 
for all 
. Show that for some 
, 
.
is differentiable and 
for all 
. Show that for some 
, 
.
4 replies
1 viewing
2. 
3. 
Bracket 2
2. 
3. 
Bracket 3![$$\int_0^{1}\frac{dx}{1-\sqrt[3]{1-\sqrt{x}}}$$](http://latex.artofproblemsolving.com/d/5/e/d5e8db00985944b2eca341e37a94e34661cb5c86.png)
2. 
3. 
Bracket 4
2. 
3. 
Bracket 5
2. 
3. 
Bracket 6
2. 
3. 
Bracket 7
2. 
3. 
Bracket 8
2. 
3. 
![$$\int_0^{2\pi}\sqrt[4]{\cos^4(x)-\cos(2x)}dx$$](http://latex.artofproblemsolving.com/7/e/e/7eebb4a488fec702e0130a253ef87f0f6dfedb2d.png)
2. ![$$\int_0^1 \frac{x^5}{\sqrt[3]{1-x^3}}dx$$](http://latex.artofproblemsolving.com/6/0/5/605bb9d81d0ccff54a276c9f7bf1c1726c136398.png)
3. 
Bracket 2
2. 
3. 
Bracket 3
2. ![$$\int_0^1 \frac{dx}{(\sqrt{x}+\sqrt[3]{x})^2}$$](http://latex.artofproblemsolving.com/6/9/8/69869c0ed754c0dfacf412ac6411742ffa164a6d.png)
3. 
Bracket 4
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Bracket 2
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D1028 : A strange result about linear algebra
Dattier 2
N
by ysharifi
Source: les dattes à Dattier
Let 
a prime number, with 
and 
, 
vector space.
Is it true that
is a group?
a prime number, with 
and 
, 
vector space.Is it true that
is a group?
2 replies
Mathematical expectation 1
Tricky123 0
X is continuous random variable having spectrum
and the distribution function is 
then
and find the expression of 
Ans:-
How to solve help me
and the distribution function is 
then
and find the expression of 
Ans:-
How to solve help me
0 replies
Double integrals
fermion13pi 1
N
by Svyatoslav
Source: Apostol, vol 2
Evaluate the double integral by converting to polar coordinates:
![\[
\int_0^1 \int_{x^2}^x (x^2 + y^2)^{-1/2} \, dy \, dx
\]](//latex.artofproblemsolving.com/e/a/9/ea9f3a093b1d4c0fa39e5b6d42afa2f71dace1e0.png)
Change the order of integration and then convert to polar coordinates.
![\[
\int_0^1 \int_{x^2}^x (x^2 + y^2)^{-1/2} \, dy \, dx
\]](http://latex.artofproblemsolving.com/e/a/9/ea9f3a093b1d4c0fa39e5b6d42afa2f71dace1e0.png)
Change the order of integration and then convert to polar coordinates.
1 reply
Roots of a polynomial not in the disc of unity
Fatoushima 1
N
by alexheinis
Show that the polynomial 
has no roots in the disc of unity.
has no roots in the disc of unity.
1 reply
Integration Bee Kaizo
Calcul8er 61
N
by Svyatoslav
Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!
61 replies
Past USAMO Medals
sdpandit 2
N
by sdpandit
Does anyone know where to find lists of USAMO medalists from past years? I can find the 2025 list on their website, but they don't seem to keep lists from previous years and I can't find it anywhere else. Thanks!
2 replies
Japanese Olympiad
parkjungmin 2
N
by parkjungmin
It's about the Japanese Olympiad
I can't solve it no matter how much I think about it.
If there are people who are good at math
Please help me.
I can't solve it no matter how much I think about it.
If there are people who are good at math
Please help me.
2 replies
Japanese high school Olympiad.
parkjungmin 0
It's about the Japanese high school Olympiad.
If there are any students who are good at math, try solving it.
If there are any students who are good at math, try solving it.
0 replies
