query: Prove that $\int_{0}^{\pi/2} \frac{\sin x}{x} dx$ converges
positive_passages.docid: 145335
positive_passages.text: Is $ \int_0^1{\frac{\sin x}{x}dx} $ convergent?
negative_passages.docid: 11387
negative_passages.text: Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
negative_passages.docid: 142854
negative_passages.text: Convergence of Integrals - A Problem
negative_passages.docid: 80553
negative_passages.text: Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
negative_passages.docid: 23368
negative_passages.text: Does $\int_1^2\frac{\sin{x}}{\log{x}} \, dx$ converge?
negative_passages.docid: 147108
negative_passages.text: Prove that $\int_0^\infty \frac{x\,\log x}{(1+x^2)^2} = 0$
negative_passages.docid: 63237
negative_passages.text: Proving that $\lim_{n \rightarrow\infty} \int_{0}^{\frac{\pi}{2}} \sin(t^n) dt =0$
negative_passages.docid: 116498
negative_passages.text: Convergence of improper integral $\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$
negative_passages.docid: 53105
negative_passages.text: How to prove that this sequence converges? $\sum_{n=1}^{\infty} \frac{1}{n\ln^2(n)}$
negative_passages.docid: 121979
negative_passages.text: Pointwise convergence of sine series of $x^{-2}$
negative_passages.docid: 58475
negative_passages.text: Does $\int_0^\infty |\cos(x^2)| \mathrm dx$ converge?
negative_passages.docid: 139297
negative_passages.text: Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$
negative_passages.docid: 129892
negative_passages.text: show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
negative_passages.docid: 38567
negative_passages.text: Convergence $I=\int_0^\infty \frac{\sin x}{x^s}dx$
negative_passages.docid: 28771
negative_passages.text: Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
negative_passages.docid: 62173
negative_passages.text: How do I show that $\int_0^\infty \frac{\sin(ax) \sin(bx)}{x^{2}} \, \mathrm dx = \pi \min(a,b)/2$
negative_passages.docid: 24056
negative_passages.text: Convergence of the improper integral $\int_{0}^{\pi/2}\tan^{p}(x) \; dx$