query: Upper bound of $\int_{-\infty}^{\infty}\sin(x)dx$.
positive_passages.docid: 68866
positive_passages.text: Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
negative_passages.docid: 147608
negative_passages.text: Cauchy principle value of $\int_{-\infty}^{\infty}\sin(x)/(x-a)dx$
negative_passages.docid: 91680
negative_passages.text: Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
negative_passages.docid: 45205
negative_passages.text: Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
negative_passages.docid: 37755
negative_passages.text: Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$
negative_passages.docid: 36366
negative_passages.text: Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
negative_passages.docid: 33675
negative_passages.text: Find $\lim_{n\to \infty} \int_n^{n+1} {\sin x \over x} dx$
negative_passages.docid: 158147
negative_passages.text: Calculating $\int_{-\infty}^{\infty}\frac{\sin(ax)}{x}\, dx$ using complex analysis
negative_passages.docid: 301
negative_passages.text: Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
negative_passages.docid: 29970
negative_passages.text: Bounds of $I=\int_0^1\frac{\sin x}{\sqrt x}$ and $J=\int_0^1\frac{\cos x}{\sqrt x}$?
negative_passages.docid: 128572
negative_passages.text: How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
negative_passages.docid: 141516
negative_passages.text: Solve $\int_0^{+\infty} \Big(\frac{\sin t}{t}\Big)^2 \ dt$
negative_passages.docid: 70845
negative_passages.text: Contour method to show that $\int_0^\infty\frac{x-\sin x}{x^3} \, dx=\frac\pi4$
negative_passages.docid: 122843
negative_passages.text: Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
negative_passages.docid: 123918
negative_passages.text: Real Analysis, Existence of a Limit Boundedly:$|\int_0^b\frac{sin(ax)}{x}dx | \le c$
negative_passages.docid: 14012
negative_passages.text: The limit of a complex integral
negative_passages.docid: 60572
negative_passages.text: Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus