A beam of length LLL carries a load w(x)=w0sin(πx/L)w(x) = w_0 \sin(\pi x / L)w(x)=w0sin(πx/L). The total load is:
w0L/πw_0 L / \piw0L/π
2w0L/π2 w_0 L / \pi2w0L/π
w0Lw_0 Lw0L
w0L2/2w_0 L^2 / 2w0L2/2