We calculate the moment functions for the beam in the state of initial load and separately for the unit load.

State with external load - state P

moment function:

\begin{aligned} &x\in (0; 10)\\ &Mp(x)=-Px\\ \end{aligned}

Unity state

moment function:

\begin{aligned} &x\in (0; 10)\\ &M(x)=-1x\\ \end{aligned}

Deflection at point A:

\begin{aligned} &EIw_A=\int_{x_p}^{x_k}(Mp(x)\cdot M(x) ) dx\\ \\ &EIw_A=\int_{0}^{10}Px^2 dx=20\cdot \frac{1}{3}\cdot 10^3\\ &w_A=\frac{6666.67}{EI}\\ \end{aligned}