$$ K \cdot w^e(x) \cdot \frac{d}{dx}T(x) \Bigg|_{x=0}^{x=L} - \int_0^L K \cdot w^e(x) \cdot \frac{d}{dx}T(x) \, dx + \int_0^L w^e(x) \cdot Q \, dx = 0 $$
I am learning Finite element analysis. In this problem the governing equation is converted to this weak form. The domain of the problem from 0 to $L$ is divided to 4 nodes with values for $T(x)$ as T1, T2, T3, T4 and for $w(x)$ as w1 w2 w3 w4. The teacher then writes something like the following, $$ w_1 \cdot \text{Expression1} + w_2 \cdot \text{Expression2} + w_3 \cdot \text{Expression3} + w_4 \cdot \text{Expression4} = 0 $$ I don't know how to arrive at this. Kindly help