The electrical voltage from a standard wall outlet is given as a function of time t by V(t) = 170 sin(120t). This is an example

The electrical voltage from a standard wall outlet is given as a function of time t by V(t) = 170 sin(120πt). This is an example of alternating current, which is electricity that reverses direction at regular intervals. The common method for measuring the level of voltage from an alternating current is the root mean square, which is given by

where T is one period of the current.
(a) Verify that T = 1/60 second for V(t) given above. 

(b) You may have seen that the voltage from a standard wall outlet is 120 volts. Verify that this is the root mean square value for V(t) given above.

Root mean square Sv(t) dt T