This white rectangle has a fixed height, \(v\), and its width \(u\) varies as a function of time, \(t\). We can write the rate of change of the width as \(\dfrac{du}{dt}\) or \(\dot{u}\). You can think of this as the speed at which the right hand edge is moving.
| The area of the white rectangle, \(A=\) | |
| In a short time interval, \(\delta t\), we can assume that \(\dot{u}\) is roughly constant, so thinking about speed and distance… | |
| The width increases by a small amount, \(\delta u =\) | |
| The area increases by the shaded area, \(\delta A =\) | |
| The rate of change of the area of the rectangle, \(\dfrac{dA}{dt} \approx \dfrac{\delta A}{\delta t} =\) | |
