query: Finding the maximum value of $\int_{0}^{1}f(x)dx$ under given conditions.
positive_passages.docid: 22294
positive_passages.text: Maximum and minimum value of $\int_0^1 f(x)dx $ given $|f'(x)|<2$
negative_passages.docid: 146266
negative_passages.text: Find the maximum value of the expression ${\frac {x}{1+x^2}} + {\frac {y}{1+y^2}}+{\frac {z}{1+z^2}}$.
negative_passages.docid: 45806
negative_passages.text: Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
negative_passages.docid: 114844
negative_passages.text: Global maxima/minima of $f(x,y,z) = x+y+z$ in $A$
negative_passages.docid: 155006
negative_passages.text: Upper bound and lower bound of an integral
negative_passages.docid: 58813
negative_passages.text: Computing $\max_{1/2 \leq x \leq 2} ( \min_{1/3 \leq y \leq 1} f(x,y) )$ where $f(x,y) = x(y \log y - y) - y \log x$.
negative_passages.docid: 154223
negative_passages.text: Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
negative_passages.docid: 87395
negative_passages.text: Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$
negative_passages.docid: 86367
negative_passages.text: Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$
negative_passages.docid: 133851
negative_passages.text: How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
negative_passages.docid: 152782
negative_passages.text: Why does finding the $x$ that maximizes $\ln(f(x))$ is the same as finding the $x$ that maximizes $f(x)$?
negative_passages.docid: 64844
negative_passages.text: Finding $E(|X_1|\ |\max |X_i| )$
negative_passages.docid: 122407
negative_passages.text: If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)dx$
negative_passages.docid: 31503
negative_passages.text: Question about Maximum Modulus Principle applied to $|f|+|g|$
negative_passages.docid: 137301
negative_passages.text: To find the minimum of $\int_0^1 (f''(x))^2dx$
negative_passages.docid: 144273
negative_passages.text: Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
negative_passages.docid: 139742
negative_passages.text: Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$