query: Prove that $f_n$ is integrable in $[0,1]$.
positive_passages.docid: 5814
positive_passages.text: Integrability of Thomae's Function on $[0,1]$.
negative_passages.docid: 42817
negative_passages.text: proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
negative_passages.docid: 30860
negative_passages.text: Prove that $f(x)=0$ in $[-1,1]$.
negative_passages.docid: 71953
negative_passages.text: If $\int_0^1 f x^n dx=0, \forall n \in \mathbb{N} $, then $f\equiv 0.$
negative_passages.docid: 14048
negative_passages.text: Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 21586
negative_passages.text: Prob. 7 (a), Chap. 6, in Baby Rudin: If $f$ is integrable on $[c, 1]$ for every $c>0$, then $\int_0^1 f(x) \ \mathrm{d}x = $ . . .
negative_passages.docid: 6990
negative_passages.text: For $f$ Riemann integrable prove $\lim_{n\to\infty} \int_0^1x^nf(x)dx=0.$
negative_passages.docid: 9957
negative_passages.text: Prove if $f:[a,b] \rightarrow \mathbb{R}$ is integrable, then so is $|f|$ and $\left|\int_{a}^{b}f(x)dx\right| \leq \int_{a}^{b}|f(x)|dx$
negative_passages.docid: 124382
negative_passages.text: Showing that $f_n:[0,1]\to\mathbb{R}$ when $f_n=nx(1-x)^n$ converges pointwise but not uniformly
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 158582
negative_passages.text: Prove that $\{\frac{\phi (n)}{n}\}_{n \in \Bbb N}$ is dense in $[0,1]$
negative_passages.docid: 76292
negative_passages.text: Showing that $f$ is identically $0$ on $\mathbb{D}$
negative_passages.docid: 5069
negative_passages.text: $GL_n(\mathbb F_q)$ has an element of order $q^n-1$
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 5229
negative_passages.text: Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.
negative_passages.docid: 31319
negative_passages.text: An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$.