Electric Charge?

Question

An electric current is given by the expression I ( t ) = 110 sin(120*pi*t), where I is in amperes and t is in seconds. What is the total charge carried by the current from t = 0 to t = 1/120 s?

I'm a little confused. I was looking at the way someone else did it. They told me that since the current is the time derivative of charge (I = dQ/dt), the charge is the integral of the current. So I did:

110sin(120*pi*(1/120))-110sin(120*pi*0) and got that the current was: 6.028 which I rounded to 6.03 for sig figs but it didn't work. Anyone see anywhere I'm going wrong?

Answer 1

Yes the total charge is an integral of 110 sin(120 pi t) dt

So Q=-[110/(120 pi)] cos (120 pi t)
evaluated from t=0 to t=1/120 sec

Q= -(110/(120 pi))[(cos (120 pi (1/120) - cos(0)]
Q= -(110/(120 pi))[(cos (pi) - cos(0)]
cos (pi) = -1
cos(0)=1 so

Q= -(110/(120 pi))[(-1 - 1]=
Q=220/(120 pi)=0.58 Coulombs