$\int^b_af(x)\,x^k \, dx=\int^b_ag(x)\,x^k \, dx$ , for all $k \in \mathbb{N}$
131876
Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
39731
The relation $a\theta_n^Sb$ iff $(\forall x\in S^n)\, xa=xb$.
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
89175
Proof of $(a+b)^{n+1}$
73489
How is the Integral of $\int_a^bf(x)~dx=\int_a^bf(a+b-x)~dx$
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
114982
How do I get that $|\int_a^b f| \le \int_a^b |f|$?
56143
Proof of a basic $AC_\omega$ equivalence
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?
133406
$n^a$ integral for all integer $n$ implies $a$ integral
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
54266
Prove that $\int_a^b \left( \int_c^d f(x,y)dy\right) dx=\int_c^d \left( \int_a^b f(x,y)dx\right) dy$