I am an engineer making a spreadsheet for beam design and i am using double integration to calculate deflection under various loads. I have made a numerical algorithm that works, but it is too slow (i'm doing thousands of calculations) so i am now trying to do it analytically. However i am stuck double integrating a trapezoidal load. Please help?
This is my problem ($\theta$ is the heaviside function, and x is my only variable, the rest are constants):
$$\int\int\theta(x-x_1)\theta(x_2-x)(q_1+(x-x_1)\frac{(q_2-q_1)}{(x_2-x_1)})\frac{(x-x_1)^2}{2}dxdx $$
I believe i have the rest sorted, but have spent days on this (i'm no mathematician!) without success :( Please help!