# Calculus Problem Book

**Average Voltage problem (calculus)?**

From the Forester calculus book:

For the normal alternating current supplied to houses, the voltage varies sinusoidally with time, making 60 complete cycles each second. Thus

V=Asin[120(pi)t]

where V = volts, t = seconds, and A = max voltage during a cycle. The nominal “110 volts” is the average of the absolute value of the voltage. Use the fundamental theorem to find the average value of y = |Asin120(pi)t| from t = 0 to t = 1/60. Use result to calculate max voltage A if the average is 110V.

I know that average velocity is v(b)-v(a)/b-a, but I don’t know how to do this. How to use fundamental theorum for it?

Will be on my test tomorrow, help will be greatly appreciated.

hmm, could you explain a little more

wait, I think I get it. Multiply integral by 2 and use 0 to 1/120, right?

I got A = 55pi…. anyone can do it and see if they get the same?

I am not sure how you are supposed to do this, but I will tell you the max voltage will be 110(sqrt2).

Also. if you work for full cycle of 0 – 1/60 you might get an average of 0 – you might need to work with 0 – 1/120.

**Stewart’s Calculus Problem 12.3.4**