query: Problem on Riemann Integration: $f(x)=\frac{1}{n}$ for $\frac1n>x\geq \frac{1}{n+1}$.
positive_passages.docid: 144942
positive_passages.text: Obtain the value of $\int_0^1f(x) \ dx$, where $f(x) = \begin{cases} \frac {1}{n}, & \frac{1}{n+1}<x\le\frac{1}{n}\\ 0, & x=0 \end{cases}$
negative_passages.docid: 139453
negative_passages.text: Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$
negative_passages.docid: 101546
negative_passages.text: Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists
negative_passages.docid: 94244
negative_passages.text: $\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
negative_passages.docid: 84785
negative_passages.text: Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
negative_passages.docid: 39073
negative_passages.text: Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
negative_passages.docid: 117640
negative_passages.text: Prove that $\lim \inf \dfrac{x_{n+1}}{x_n}\leq \lim \inf x_n^{1\over n} \leq \lim \sup x_n^{1\over n} \leq \lim \sup \dfrac{x_{n+1}}{x_n}. $
negative_passages.docid: 63016
negative_passages.text: Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$
negative_passages.docid: 30219
negative_passages.text: Sufficient condition(s) for $f'$ to be Riemann integrable
negative_passages.docid: 38226
negative_passages.text: Question about the Riemann-Lebesgue Lemma proof
negative_passages.docid: 18153
negative_passages.text: To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
negative_passages.docid: 104691
negative_passages.text: Integration of $\int_{0}^{1} \frac{x^k}{1-x} dx$
negative_passages.docid: 69978
negative_passages.text: Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
negative_passages.docid: 52293
negative_passages.text: The equivalence of definitions Riemann integral
negative_passages.docid: 146528
negative_passages.text: Define $I_n=\int_0^1\frac{x^n}{\sqrt{x^2+1}}dx$ for every $n\in\mathbb{N}$. Prove that $\lim_{n\to\infty}nI_n=\frac{1}{\sqrt 2}$.
negative_passages.docid: 138174
negative_passages.text: Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$
negative_passages.docid: 4971
negative_passages.text: $\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$