The derivative of $\int_0^xxf(t)dt$ and why we cannot treat $xf$ as continuous.
109561
Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
32694
Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.
127114
Differentiability implying continuity
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
21339
IF $f(x) = \int_{0}^{\phi (x)} g(t) dt$, How could we find $f'(x)$?
105767
derivative under integral intuition
157347
continuity, discontinuity derivative and relation to being derivative but its partials are not continuous
135449
Prove: $\frac1x$ is not a uniformly continuous function
124499
Where is the error in my proof that all derivatives are continuous?
49511
Do we have $\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$?
65876
A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
97553
Continuity of $\frac{2xy}{x^2+y^2}$ at $(0,0)$
59165
Derivative of a linear transformation.
90325
Why use the derivative and not the symmetric derivative?
103241
A function that is continuous at the origin but not differentiable there