Let $f(t)$ be a continuous function on an interval [a,b]. If $\int_a^b |f(t)| dt = 0$, then determine $f(t)$.
138742
Why must the integral of a nonzero continuous function be nonzero?
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
92685
Let $f:[0,1]\to\mathbb{R}$ be a continuous function. Calculate $\lim\limits_{c\to 0^+} \int_{ca}^{cb}\frac{f(x)}{x}\,dx$
44269
If $f$ is nonnegative and continuous on $[a,b]$, then $\left(\int_a^b f(x)^n \ dx\right)^{1/n}\to\max\limits_{[a,b]} f$
157308
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be continuous.Let $t\in\mathbb{R}$. Evaluate:$\lim_{h\rightarrow0}\frac{1}{h}\int_{t-h}^{t+h}f(s)ds$
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
12240
Problem with a continuous function
69301
If $\int_{0}^{x}f(t)dt\rightarrow \infty$ as $|x|\rightarrow \infty\;,$ Then every line $y=mx$ Intersect $ y^2+\int_{0}^{x}f(t)dt=2$
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
12498
Derivable function on an interval $ [a,b]$ with derivative unbounded on $[a,b]$
84092
If $id:(X,d_1)\to (X,d_2)$ is continuous then what will be $X$?
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
151410
Inequality of continuous functions
13852
Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone