Prove there exists $[a,b] \subset [0,1]$ such that $\int_a^b f(x)\,dx=\int_a^b g(x)\,dx=\frac{ 1}n$
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
40047
Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
104855
Prove that $N \subset Z(G)$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
63251
Evaluation of $\int^1_0\frac{x^b-x^a}{\ln x} d x=\ln{{\frac{1+b}{1+a}}}$
71071
Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
7903
Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
114982
How do I get that $|\int_a^b f| \le \int_a^b |f|$?
136966
Riemann integral proof $\int^b_a f(x) \, dx>0$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power