Let $f : [a,b] \rightarrow \mathbb{R}$ be continuous, such that $f(x) ≥ 0$. Show that if $\int^b_a{f(x)dx} = 0$ then $f(x) =0$
48314
Show that if a function is not negative and its integral is $0$ than the function is $0$
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
61500
If f is continous and exist real numbers show that $f(x)=0$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
76790
Condition to guarantee $f=0$ on $[a,b]$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
33081
If $\int_{\Bbb R^2}|f(x+iy)|\,dx\,dy<\infty$ then prove that $f\equiv 0$
138054
Proving that $\int_0^1 f(x)e^{nx}\,{\rm d}x = 0$ for all $n\in\mathbb{N}_0$ implies $f(x) = 0$
153957
Bounded variation and $\int_a^b |F'(x)|dx=T_F([a,b])$ implies absolutely continuous
127868
If $f$ is nonnegative and integrable then $F(x) = \int_{-\infty}^x f$ is continuous.
21301
If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
136966
Riemann integral proof $\int^b_a f(x) \, dx>0$
103495
Let $f$ be continuous. Then $\int_{0}^{x}\left[\int_{0}^{t}f\left(u\right)du\right]dt=\int_{0}^{x}f\left(u\right)\left(x-u\right)du$