## Sideways

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, $\dfrac{dA}{dt} \approx \dfrac{\delta A}{\delta t} =$