How to show $\int_0^1 f^3 dx < ( \int_0^1 f dx )^2 $
128189
Proving Integral Inequality
94869
Show that $ \int_{k}^{2} \frac{1}{f(y)} =1$
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
20415
Show that the integral of a positive function is positive
78174
How prove this inequality $\left(\int_{0}^{1}f(x)dx\right)^2\le\frac{1}{12}\int_{0}^{1}|f'(x)|^2dx$
158180
An inequality of $\int_0^1 |f(x)|dx$
97579
showing a function defined from an integral is entire
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
117246
Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$.
113066
Calculate $\int_0^1f(x)dx$
58647
Show that $f$ is integrable and $\int_{I} f=0$
131120
Proving an integral equation.
5180
How to show $\alpha\int_a^cf(x)dx+\beta \int_c^b f(x)dx =0$ means $f(x)=0$ everywhere $?$
22294
Maximum and minimum value of $\int_0^1 f(x)dx $ given $|f'(x)|<2$
71071
Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
115335
How can we prove this integral inequality?