Derive the expression for the moment coefficient about the leading edge [Equation (1.17)] from the expression for the moment about the leading edge [Equation (1.11)].

\(\begin{aligned} 1.11:   M_{\mathrm{LE}}^{\prime}= & \int_{\mathrm{LE}}^{\mathrm{TE}}\left[\left(p_u \cos \theta+\tau_u \sin \theta\right) x-\left(p_u \sin \theta-\tau_u \cos \theta\right) y\right] d s_u \\ & +\int_{\mathrm{LE}}^{\mathrm{TE}}\left[\left(-p_l \cos \theta+\tau_l \sin \theta\right) x+\left(p_l \sin \theta+\tau_l \cos \theta\right) y\right] d s_l\end{aligned}\)

\begin{aligned}
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}