$\newcommand{\a}[1]{\langle#1\rangle}$ As you can see, the left end of the beam is fixed, and a distributed load is applied to the beam. I calculated the shear forces by conventional means, but when I calculate it with singularity function I get weird results. Here are my calculations:
$$q(x)=-3000\a{x-0}^{-2} + 3000\a{x-0}^{-1} - \frac{2000}{3}\a{x-0}^1 + \frac{2000}{3}\a{x-0}^0$$
The first term comes from reaction torque and the second term comes from reaction normal force. The shear force is just the integral of the $q(x)$.
$$v(x) = 3000\a{x-0}^{-1} - 3000\a{x-0}^{0} + \frac{2000}{6}\a{x-0}^2 - \frac{2000}{3}\a{x-0}^1$$
As you can see the results are false. I'll appreciate any help.