#### Answer

The charge that passes through between 0 and 10 milliseconds is: 0 Coulombs
The charge that passes through between 0 and 15 milliseconds is: 15.9 mC

#### Work Step by Step

We know the following equation for charge:
$Q = \int_{t_0}^{t} idt$
Using substitution, we obtain:
$ Q = \int_{0}^{.01} 5sin(200 \pi t)dt \\ Q = 0$
We now solve for the charge from 0 to 15 milliseconds using the same process:
$ Q = \int_{0}^{.015} 5sin(200 \pi t)dt $
Using a calculator to evaluate this integral, we find:
$ Q = 15.9\ mC$