A signal generator in a school laboratory produces a voltage v = 3 sin 2t volts, where t is the…

A signal generator in a school laboratory produces a voltage $v = 3\sin 2t$ volts, where $t$ is the time in seconds. The area between the voltage graph and the time axis has the unit volt second. A technician records the signal from $t = 0$ to $t = \dfrac{3\pi}{2}$ seconds, which is one and a half cycles of the wave. She wants two numbers from the record. The first is the net area, which counts the part of the graph below the time axis as negative. The second is the total area, which counts every part of the graph as positive. The net area is useful when the direction of the voltage matters, and the total area is useful when only its size matters. The record is used to test a new data logger, and the logger must report both quantities correctly. The technician will check its output against her own hand calculation. Find both numbers, in volt seconds.