query: Estimate the lower bound of the following integral.
positive_passages.docid: 21301
positive_passages.text: If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
negative_passages.docid: 151400
negative_passages.text: Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$
negative_passages.docid: 75577
negative_passages.text: Double integral over a typical region.
negative_passages.docid: 129578
negative_passages.text: A result of Stieltjes Integral
negative_passages.docid: 1234
negative_passages.text: Evaluating limits of integrals
negative_passages.docid: 44817
negative_passages.text: Lower bound on energy is potential minimum
negative_passages.docid: 154612
negative_passages.text: $\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
negative_passages.docid: 115533
negative_passages.text: Inequality for small values of $t$
negative_passages.docid: 158180
negative_passages.text: An inequality of $\int_0^1 |f(x)|dx$
negative_passages.docid: 7192
negative_passages.text: Integral inequality with a strange condition
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 78444
negative_passages.text: Limit of definite integral of $f(x)\cos(mx)$
negative_passages.docid: 95571
negative_passages.text: Integral of a Gaussian process
negative_passages.docid: 116778
negative_passages.text: Calculation of an integral via residue.
negative_passages.docid: 103374
negative_passages.text: A Problem on Improper Integrals
negative_passages.docid: 137301
negative_passages.text: To find the minimum of $\int_0^1 (f''(x))^2dx$
negative_passages.docid: 57167
negative_passages.text: A hard problem on exponential integration