Επίλυση ∫ (from 0 to pi / 2) of frac{-frac{m_{0}R^{2}}{2}(1-cosθ)+fR^3/4(1-cosθ)^2}{1/12omegae^3(D-θ)^3}dθ

$$\int _ { 0 } ^ { \pi / 2 } \frac { - \frac { m _ { 0 } R ^ { 2 } } { 2 } ( 1 - \cos \theta ) + \frac { f R ^ { 3 } } { 4 } ( 1 - \cos \theta ) ^ { 2 } } { \frac { 1 } { 12 } \omega e ^ { 3 } ( D - \theta ) ^ { 3 } } d \theta$$

Διαφόριση ως προς m_0

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(\int _{0}^{\frac{\pi }{2}}\frac{3R^{2}\left(-\cos(\theta )+1\right)\left(-Rf\cos(\theta )+Rf-2m_{0}\right)}{\omega \left(e\left(D-\theta \right)\right)^{3}}\mathrm{d}\theta )$$