query: About the proof of the inequality: $\int_0^1 |f(x)|dx\le\text{max}\left(\int_0^1 |f’(x)|dx, \left\vert\int_0^1 f(x)dx\right\vert\right)$
positive_passages.docid: 158180
positive_passages.text: An inequality of $\int_0^1 |f(x)|dx$
negative_passages.docid: 50273
negative_passages.text: How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
negative_passages.docid: 128171
negative_passages.text: Proof for Integral Inequality $|\int f| \le \int |f|$ - is it sufficient enough?
negative_passages.docid: 20192
negative_passages.text: Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
negative_passages.docid: 66404
negative_passages.text: Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
negative_passages.docid: 33617
negative_passages.text: Prove the inequality involving multiple integrals
negative_passages.docid: 53748
negative_passages.text: Find maximum value of $\int_{0}^{1}\left(f(x)\right)^3dx$
negative_passages.docid: 19658
negative_passages.text: $\max_{t\in[0,T]}|x(t)|^2 \le |x(0)|^2e^{\int_0^T|y|^2\,\mathrm ds}.$ using gronwall's lemma?
negative_passages.docid: 93806
negative_passages.text: $\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
negative_passages.docid: 110368
negative_passages.text: Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$
negative_passages.docid: 46844
negative_passages.text: Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$
negative_passages.docid: 77130
negative_passages.text: How to prove this inequality $\left|x\sin{\frac{1}{x}}-y\sin{\frac{1}{y}}\right|<2\sqrt{|x-y|}$?
negative_passages.docid: 114184
negative_passages.text: Show: $\sum_{k=1}^{\infty}\mu(\left\{f\geq k\right\})\leq\int f\, d\mu\leq\sum_{k=0}^{\infty}\mu(\left\{f>k\right\})$
negative_passages.docid: 51347
negative_passages.text: Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$
negative_passages.docid: 91740
negative_passages.text: Hadamard's inequality proof
negative_passages.docid: 20415
negative_passages.text: Show that the integral of a positive function is positive
negative_passages.docid: 99753
negative_passages.text: How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?