Reputation
2,249
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
Badges
9 29
Impact
~24k people reached

12h
revised How to evaluate this indefinite integration $\int \frac{\tan^4 \theta d \theta}{1-\tan^2 \theta}$?
added 18 characters in body
15h
comment use parseval's identity to evaluate the integral $ \int_{-\pi}^{\pi}\sin^4 xdx$
Call me crazy, but I would wrote that in reverse order, that is $\pi \cdot \frac{1}{4} + ...$, because $a_0=\frac{1}{2}$. I mean, your answer is correct, but... That just me. And oh, yes, answer is $3\pi/4$, or?
16h
comment Feynman technique of integration for $\int^\infty_0 \exp\left(\frac{-x^2}{y^2}-y^2\right) dx$
Just for note: There is similar, but harder problem, when you have $dy$ instead of $dx$. If you want to solve that problem (where $x$ is parameter, say $x>0$ (but you can do all for $x \in \mathbb{R}$)), first find $I'(x)$ and then use substitution $y \mapsto \frac{x}{t}$ for $I(x)$, where $I(x)$ is your integral. You should end with something like $I'(x)+2I(x)=0$, that is $I(x)=Ce^{-2x}$ (you can find that $C=\frac{\sqrt{\pi}}{2}$ from $I(0)=\lim_{x \to 0^+} I(x)$).
May
6
answered Show that holomorphic function $f: \mathbb{C} \rightarrow \mathbb{C}$ is constant
Apr
25
reviewed Approve Is the $C^0$-fine topology finer than the metric topology?
Apr
2
reviewed Approve In $P^n$(projection of $C^{n+1}$) is a variety isomorphic to $P^1$ irreducible?
Mar
30
reviewed Approve how to calculate what I need for final exam
Jan
26
comment Show that if $v\in (V_c)^{\perp}$ then $(Av)\in (V_c)^{\perp}$ for a normal matrix $A$ with an eigenvalue $c$
$\langle x, Av \rangle = \langle x, v c \rangle = ....$
Jan
25
reviewed Approve Bounding summations
Jan
23
awarded  Good Question
Jan
21
reviewed Approve Evaluating the limit $\displaystyle \lim _{x\to \infty }\frac{(x^2+1)}{(x-1)}\sin(\frac{1}{x})$
Jan
17
reviewed Reject What is the intuition behind the exponential distribution?
Jan
15
comment Proving compactness of an operator
You can use ideas from this question math.stackexchange.com/questions/320751/….
Jan
15
reviewed Approve on the definition of graded Betti numbers
Jan
15
comment Show that $|z+w|^2$ + $|z-w|^2$ = $2|z|^2 + 2|w|^2$
This is Parallelogram law.
Jan
12
comment Bounding $\frac{2}{\pi}\int_0^{\pi}\frac{|\sin(n+\frac{1}{2})t|}{2\sin\frac{1}{2}t}$ below by $\frac{4}{\pi^2}\log n$
From which book is this?
Jan
9
awarded  Yearling
Dec
28
reviewed Approve Likelihood Ratio and Neyman-Pearson factorization theorem
Dec
28
reviewed Reject Prove that $\frac{\sin n}{n}$ is a Cauchy sequence from the definition.
Dec
28
answered $f(x):S^{2n} \rightarrow S^{2n}$ continuous so that there is $x \in S^{2n}$ with $f(x)=x$ or $f(x)=-x$