Calculus/Work

$\begin{array}{cc}W=\int Fdr& =\int madr\\ & =\int m\frac{dv}{dt}dr\\ & =m\int \frac{dr}{dt}dv\\ & =m\int vdv\\ & =\frac{m{v}^2}{2}=\mathrm{\Delta }{E}_k\end{array}$