At a critical junction in a supercomputer, the current as a function of time is given as

i(t) = 3t^2-2t, where i is measured in milliamps and t is measured in seconds. How much charge passes through this critical junction during the interval 0 < t < 5.00 s?

To determine the amount of charge passing through the critical junction during the given interval, we need to calculate the integral of the current function with respect to time.

The integral of the current function i(t) = 3t^2 - 2t represents the accumulated charge over time. Let's calculate it step by step:

1. Identify the integral bounds: We are interested in the interval 0 < t < 5.00 s.

2. Calculate the indefinite integral:
∫(3t^2 - 2t) dt = t^3 - t^2 (We omit the constant of integration because it will cancel out in the next step.)

3. Evaluate the definite integral using the bounds:
∫[0 to 5](3t^2 - 2t) dt = [t^3 - t^2] evaluated from 0 to 5
= [(5)^3 - (5)^2] - [(0)^3 - (0)^2]
= [125 - 25] - [0 - 0]
= 100

Therefore, the amount of charge passing through the critical junction during the interval 0 < t < 5.00 s is 100 milliCoulombs.