For a charge function $Q\left(t\right)$, the instantaneous current at time $t$ is defined as

Which expression gives the total charge transferred between times $t_1$ and $t_2$ when the current varies with time?

The current in a sensor lead is $I\left(t\right)=6t$ $\text{A}$. How much charge passes through the lead from $t=0$ to $t=3$ $\text{s}$?

A uniform current density of $50$ ${\text{A/m}}^2$ crosses a flat surface of area $0.020$ ${\text{m}}^2$. The angle between $\overrightarrow{J}$ and the surface normal is $60$°. What current passes through the surface?

A detector window has area $4.0$ ${\text{cm}}^2$. A uniform current density $J\left(t\right)=100t$ ${\text{A/m}}^2$ is normal to the surface for $0\le t\le 2.0$ $\text{s}$. Approximately how many electrons pass through the window during that time?