If $f$ is a periodic function with period $L$, show that the integral $\int_{a}^{a+L}f(x)dx$ is independent of a.
127953
Integral of periodic function over the length of the period is the same everywhere
37015
Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
158180
An inequality of $\int_0^1 |f(x)|dx$
54499
How do I show that all continuous periodic functions are bounded and uniform continuous?
98344
Prove that $\int_0^1[f''(x)]^2dx\ge4.$
46844
Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$
62268
Doubly periodic entire function with periods that are linearly independent over $\mathbb{Q}$ is constant.
91744
Proving sum of sines is periodic when ratio of their frequencies is rational using differentation
136966
Riemann integral proof $\int^b_a f(x) \, dx>0$
69656
Prove or disprove that $\int_a^b |f(x)|\ \mathrm{d}x\geq \big | \int_a^b f(x)\ \mathrm{d}x\big| $
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
49884
Integral vanishes on all intervals implies the function is a.e. zero
96495
Periodicity of a Function Given the Functional Equation $f(x+a)=\frac12+\sqrt{f(x)-\big(f(x)\big)^2}$
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
22864
Show that $\int_{a}^{b} |f|^2\le\frac{(b-a)^2}{2}\int_{a}^{b} |f'|^2$
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
3978
How can you prove that a function has no closed form integral?