If $g(x)=\int_1 ^3f(x+t)dt$ what will be the value of $g'(0)$
140259
Find the value of $g'(0)$.
109561
Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
84413
Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?
98741
Finding $\int_{0}^{\frac{\pi}{4}} \frac{\tan \theta - \tan^3 \theta}{\ln \tan \theta}$
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
74100
How do you solve $f'(x) = f(f(x))$?
103495
Let $f$ be continuous. Then $\int_{0}^{x}\left[\int_{0}^{t}f\left(u\right)du\right]dt=\int_{0}^{x}f\left(u\right)\left(x-u\right)du$
77133
$g'(x) = \frac{1}{x}$ for all $x > 0$ and $g(1) = 0$. Prove that $g(xy) = g(x) + g(y)$ for all $x, y > 0$.
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
91775
Show that $\int_0^1 f^2(x)dx\geq 3$, if $f:[0,1]\to \mathbb{R}$ is an integrable function s.t. $\int_0^1 f(x)dx=\int_0^1 xf(x)dx=1$
104848
What's the name of this theorem ($f>g$ given $f'>g'$ and initial value)?
49511
Do we have $\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$?
111705
Why does $\frac{1+t}{(1-t)^3}=\sum_{n=0}^{\infty}(1+n)^2t^n$
153612
Finding $g_i:\mathbb{R}^n\to\mathbb R$ s.t $f(x)=\sum\limits_{i=1}^nx_i\cdot g_i(x)$
21339
IF $f(x) = \int_{0}^{\phi (x)} g(t) dt$, How could we find $f'(x)$?
137060
Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
132124
$\int_{0}^{\infty}\frac{x}{x^3+1}dx$ =?