Before starting this example, please read a short Theoretical introduction

We write the moment functions, calculate the derivative with respect to the force corresponding to the sought displacement

\begin{aligned} &x\in (0; 10)\\ &Mg(x)=-Px\\ &\frac{\partial Mg(x)}{\partial P}=-x\\ \end{aligned}

We calculate the displacement

\begin{aligned} &EIw_A=\int_{0}^{L}(Mg(x)\cdot \frac{\partial Mg(x)}{\partial P}) dx\\ &for\ P=20\\ &EIw_A=\int_{0}^{10}20x^2 dx=20\cdot \frac{1}{3}\cdot 10^3\\ &w_A=\frac{6666.67}{EI}\\ \end{aligned}