Definite Integration prove max of $f'(x)\ge \text{something should go here}$
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
154247
Proving $f(x)$ attains $\max$ or $\min$ when $f(x)\to0$ as $|x|\to\infty$.
44269
If $f$ is nonnegative and continuous on $[a,b]$, then $\left(\int_a^b f(x)^n \ dx\right)^{1/n}\to\max\limits_{[a,b]} f$
110208
limit of integral $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$
37015
Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
113255
$X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.
115335
How can we prove this integral inequality?
40936
How prove this integral inequality
64844
Finding $E(|X_1|\ |\max |X_i| )$
79024
the derivation of E(X|X)
121406
Interesting Integration with respect to $[x]$ where $[\cdot]$ is greatest integer function
95626
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
150699
Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$
37192
proof of the second generalized mean value theorem for integrals
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
158180
An inequality of $\int_0^1 |f(x)|dx$
95288
Prove that, $f'(0) \ge -\sqrt{2}$ for a function $f$ satisfying some conditions on $(-1,1)$.