query: if $f(x)>0$ then $\int_{a}^{b}f(x)dx>0$
positive_passages.docid: 18261
positive_passages.text: Prove $\int_{a}^{b}{f(x)dx}>0$.
negative_passages.docid: 94971
negative_passages.text: For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$
negative_passages.docid: 51659
negative_passages.text: If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
negative_passages.docid: 145424
negative_passages.text: If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.
negative_passages.docid: 44269
negative_passages.text: If $f$ is nonnegative and continuous on $[a,b]$, then $\left(\int_a^b f(x)^n \ dx\right)^{1/n}\to\max\limits_{[a,b]} f$
negative_passages.docid: 58647
negative_passages.text: Show that $f$ is integrable and $\int_{I} f=0$
negative_passages.docid: 21954
negative_passages.text: A question about $f(x)\equiv 0$
negative_passages.docid: 88690
negative_passages.text: $\int_a^b f(x)\mathrm dx=0$ for all $-\infty<a<b<\infty$ a,b rational implies $f=0$ a.e
negative_passages.docid: 150502
negative_passages.text: If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$
negative_passages.docid: 131876
negative_passages.text: Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
negative_passages.docid: 138544
negative_passages.text: For which values of $x$, will $f (x) . f '(x) < 0$?
negative_passages.docid: 89537
negative_passages.text: $ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
negative_passages.docid: 72660
negative_passages.text: How can I show that $f$ must be zero if $\int fg$ is always zero?
negative_passages.docid: 90369
negative_passages.text: Does $\int_a^bf(x) = 0$ imply $f(x) = 0$ for a Riemann Integral function?
negative_passages.docid: 45602
negative_passages.text: Show that is $\int_A f$ exists, then so does $\int_A |f|$
negative_passages.docid: 76790
negative_passages.text: Condition to guarantee $f=0$ on $[a,b]$
negative_passages.docid: 69695
negative_passages.text: $f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$