Maximum value of $\int_0^1(f(x))^3 dx$ if $|f(x)|\leq 1$ and $\int_0^1 f(x)dx=0$.
88580
Finding the maximum value of $\int_0^1 f^3(x)dx$
104510
For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
31503
Question about Maximum Modulus Principle applied to $|f|+|g|$
67625
$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$
129343
What is the maximum value of $|f(z)|$ on the unit disc $D=\{z \in \mathbb C:|z|\leq 1\}$?
70790
Evaluation of $\lim_{q \to 0} (\int_0^1 |f|^q)^{1/q} $ for $f \in L^1([0,1])$.
150502
If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$
128171
Proof for Integral Inequality $|\int f| \le \int |f|$ - is it sufficient enough?
53378
$\max(\{n: n+5 | n^5 + 5\})$
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
27062
Given complex $|z_{1}| = 2\;\;,|z_{2}| = 3\;\;, |z_{3}| = 4\;\;$ : when and what is $\max$ of $|z_{1}-z_{2}|^2+|z_{2}-z_{3}|^2+|z_{3}-z_{1}|^2$
133851
How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
137301
To find the minimum of $\int_0^1 (f''(x))^2dx$
21301
If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
100869
How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$
71071
Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
86367
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$