Finding the maximum value of $\int_0^1 (f(x))^3 dx$, given certain conditions on $f(x)$ and $\int_0^1 f(x) dx$
53748
Find maximum value of $\int_{0}^{1}\left(f(x)\right)^3dx$
127032
Maximum of $\cos \alpha_{1}\cdot \cos \alpha_{2}\cdot \cos \alpha_{3}....\cos \alpha_{n}.$
64844
Finding $E(|X_1|\ |\max |X_i| )$
113066
Calculate $\int_0^1f(x)dx$
79125
How to find the maximum value for the given $x\cos{\lambda}+y\sin{\lambda}$?
87395
Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$
129399
Maximum module principle
56958
bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
127634
query on maximum minimum of multi-variable function
33389
What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
154223
Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
71071
Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
6552
Evaluation of the double integral $\int_{[0,1]×[0,1]} \max\{x, y\} dxdy$
155415
Minimax problem for optimization $\inf \sup \frac{x f(x)}{\int_0^1 f(t) dt}$
57785
Finding all maxima and minima of a function
76209
Inequalities for combinations of $\int f $ and $\int (1/f)$ where $m\le f\le M$ on an interval
91775
Show that $\int_0^1 f^2(x)dx\geq 3$, if $f:[0,1]\to \mathbb{R}$ is an integrable function s.t. $\int_0^1 f(x)dx=\int_0^1 xf(x)dx=1$