$\int_{-\infty}^{\infty} x^pf(x)=0$ for all $p\geq 0$, how to prove $f=0$ with the Fourier transform?
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
33989
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
301
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
90369
Does $\int_a^bf(x) = 0$ imply $f(x) = 0$ for a Riemann Integral function?
40537
How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
42817
proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
67292
Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
89421
Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?
100711
$\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$
80060
Is $\frac{1}{\infty}$  equal zero?
16053
Generalized Fresnel integral $\int_0^\infty \sin x^p \, {\rm d}x$
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
47211
Does $\varphi(x)\le\int_0^x\varphi(t)dt$ for all $x\in[0,\infty)$ imply $\varphi\equiv0$.