If $\int^x_0 f (t) dt =x+ \int^1_x t f (t) dt$, find value of $f(1)$
34790
Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
95429
If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
64339
Find $f$ where $f'(x) = f(1+x)$
144146
find a $\int_{x}^{g(x)} f(t)\,dt = 1$
133851
How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
20904
Finding derivative of this integral function.
101267
Show: $\int f\, d\mu=\int\limits_0^{\infty}\mu(\left\{x\in X: f(x)>t\right\})\, dt$
81437
Find the value of $y(1)$ of the ODE $y'+y=|x|$.
104510
For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
33989
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
122407
If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)dx$
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
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 $f(1) = 3$
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$