Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
67565
If $\int^x_0 f (t) dt =x+ \int^1_x t f (t) dt$, find value of $f(1)$
86367
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$
151958
How to show $f'(0)$ exist and is equal to $1$?
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
48651
Prove that $\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}$ for positive $p$ and $q$
59063
$f(f(x))=f(x)$ question
67322
evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
109790
Finding the value of $\int_0^{\pi/2} \frac{dt}{1+(\tan(x))^{\sqrt{2}}}$
97253
How prove $e^x|f(x)|\le 2$ if $f(x)=\int_{x}^{x+1}\sin{(e^t)}dt$
109561
Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
144146
find a $\int_{x}^{g(x)} f(t)\,dt = 1$
157504
What type of differential equation is $f'(x) = f(x/2)$ and how do you solve it?
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
13042
Finding a function from the given functional equation .
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
109099
Prove that $\lim_{h \to 0}\frac{1}{h}\int_0^h{\cos{\frac{1}{t}}dt} = 0$
147195
Help needed in finding the value of $f(2001)$ in the given functional equation