I've been given a problem in my electrical engineering class which is confusing me.
I'm given $i(t) = 5\sin(6 \pi t/\mathrm s)\, \mathrm{mA}$ (mA is mC/s) and I need to find the total charge transferred from $0$ to $1\,\mathrm s$.
$i = \frac{\mathrm dq}{\mathrm dt}$, so I take the definite integral of $i$ over $0\,\mathrm s\le t \le 1\,\mathrm s$.
Unfortunately, while I know how to do this without units, with units is confusing me, especially the way it's written since $t/\mathrm s$ would look like 1/second when $t$ is 1...
The result should be in mC (or possibly some other magnitude of C).
Since $t$ is a time, it is measured in a time unit, for example seconds. Thus after dividing by the time unit $t$, we obtain a dimensionless number, which is just the right thing to feed into the sine function. After multiplication with the current unit mA, we do indeed have a current. Then integrating over time give us a charge. That should be fine. $$ \int_{0\,\mathrm s}^{1\,\mathrm s} 5 \sin\frac{2\pi t}{\mathrm s}\,\mathrm{mA}\,\mathrm dt=5\,\mathrm{mC}\cdot \int_{0\,\mathrm s}^{1\,\mathrm s} \sin\frac{2\pi t}{\mathrm s}\,\frac{\mathrm dt}{\mathrm s}=5\,\mathrm{mC}\cdot \int_{0}^{1} \sin{2\pi \tau}\,\mathrm d\tau$$ if you prefer.