query: Proving an Integral Identity with Increasing Bounds
positive_passages.docid: 3704
positive_passages.text: Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
negative_passages.docid: 135571
negative_passages.text: Bézout Identity with coefficient divisibility constraints
negative_passages.docid: 112517
negative_passages.text: Proving bounds of a harmonic series
negative_passages.docid: 90343
negative_passages.text: Proving the inequality $|e^z-1|\leq e^{|z|}-1$
negative_passages.docid: 118613
negative_passages.text: Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
negative_passages.docid: 108560
negative_passages.text: Proof of a Gaussian Integral property
negative_passages.docid: 15237
negative_passages.text: Prove an inequality using complex analysis
negative_passages.docid: 19078
negative_passages.text: Prove an interpolation inequality
negative_passages.docid: 123186
negative_passages.text: Proving the probability integral transform without assuming that the CDF is strictly increasing
negative_passages.docid: 7192
negative_passages.text: Integral inequality with a strange condition
negative_passages.docid: 145900
negative_passages.text: Proof of a double summation reduction identity
negative_passages.docid: 158180
negative_passages.text: An inequality of $\int_0^1 |f(x)|dx$
negative_passages.docid: 40420
negative_passages.text: Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
negative_passages.docid: 126632
negative_passages.text: Proving Inequalities with Absolute values
negative_passages.docid: 4656
negative_passages.text: Prove that there is a $\delta$ such that $\int_{0}^{1} (f(x))^2dx\leq \delta$$\int_{0}^{1} (f'(x))^2dx$ for all $f$ with these conditions
negative_passages.docid: 123757
negative_passages.text: Proving a summation inequality with induction
negative_passages.docid: 6449
negative_passages.text: Prove logarithmic inequality with greatest integer function.