`f(x)=int_0^x f(t) dt=x+int_x^1 tf(t)dt,` then the value of `f(1)` is

Options

A. `1//2`
B. 0
C. 1
D. `-1//2`

Explanation

To solve the problem, we start with the given equation:

\[ f(x) = \int_0^x f(t) \, dt = x + \int_x^1 t f(t) \, dt \]

### Step 1: Differentiate both sides
We will differentiate both sides of the equation with respect to \(x\). Using Leibniz's rule for differentiation under the integral sign, we have:
...