Continuous positive function such that $\int\limits_1^{\infty}f(x)dx$ converges, while $\int\limits_1^{\infty}f^2(x)dx$ diverges
87115
Find a continuous function $f:[1,\infty)\to\Bbb R $ such that $f(x) >0 $, $\int_1^\infty f(x)\,dx $ converges and $\int_1^\infty f(x)^2\,dx$ diverges
140445
Sequence of continuous functions whose pointwise limit is discontinuous
88792
Convergence of $\int_0^\infty $sin$ (x^p) dx$
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
19072
$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
91680
Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
91616
Existence of a $C_c^{\infty}$ function $\Phi$ s.t. $\int \nabla \Phi \neq 0.$
21301
If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
13674
Divergence of an improper integral
90558
A question related to a convergence of an integral
47857
Find the Values of $p$ and $q$ such that $\int_0^{\infty} x^p\ln(1+x)^q dx$ Converges or Diverges.
71140
Pointwise limit of the sequence of continuously differentiable functions defined inductively.
96273
Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
52177
divergence/convergence $\sum_{k=1}^{\infty} \frac{1}{5k+2}$
56867
Convergence proof that involves integral
135999
One sided limit of an increasing function defined on an open interval
145233
How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?