Starting with Equations (1.7), (1.8), and (1.11), derive in detail Equations (1.15), (1.16), and (1.17).

\begin{aligned}
1.15:  
c_n= & \frac{1}{c}\left[\int_0^c\left(C_{p, l}-C_{p, u}\right) d x+\int_0^c\left(c_{f, u} \frac{d y_u}{d x}+c_{f, l} \frac{d y_l}{d x}\right) d x\right] \\
1.16:  
c_a= & \frac{1}{c}\left[\int_0^c\left(C_{p, u} \frac{d y_u}{d x}-C_{p, l} \frac{d y_l}{d x}\right) d x+\int_0^c\left(c_{f, u}+c_{f, l}\right) d x\right] \\
1.17:  
c_{m_{\mathrm{LE}}}= & \frac{1}{c^2}\left[\int_0^c\left(C_{p, u}-C_{p, l}\right) x d x-\int_0^c\left(c_{f, u} \frac{d y_u}{d x}+c_{f, l} \frac{d y_l}{d x}\right) x d x\right. \\
& \left.+\int_0^c\left(C_{p, u} \frac{d y_u}{d x}+c_{f, u}\right) y_u d x+\int_0^c\left(-C_{p, l} \frac{d y_l}{d x}+c_{f, l}\right) y_l d x\right]
\end{aligned}