The slope at A is calculated at $x = 0$.

The given units are $EI = 10 \times 10^{13} \text{ Nmm}^2$. The loads are given in kN, so they must be converted to N (multiply by $10^3$).

The deflection equation includes a constant of integration $C_1$ (implicitly 0 based on the provided equation).

Evaluating $EI \theta$ at $x = 0$ results in the initial slope value.

Efficient for beams with discontinuous loading

Eliminates the need to find constants of integration for every segment

Can be algebraically tedious for complex loading

Sign convention must be strictly followed

Structural analysis of simply supported beams

Calculation of deflection and slope in determinate structures

Equation: $EI \theta = -\frac{5}{2}x^2 + \frac{15}{2}(x - 6)^2 + C_1$.

At $x=0$, $EI \theta = 0 + 0 + C_1$. From the given $EIy$ equation, the constant of integration $C_1$ is $-30$ (calculated from boundary conditions). Thus, $\theta_A = \frac{-30 \times 10^9}{10 \times 10^{13}} = -0.0003$ radians. The magnitude is $0.0003$ radians.