+227 Alright, here's my problem:
22. Home Electricity Use The rate at which your home consumes electricity is measured in kilowatts. If your home consumes electricity at the rate of 1 kilowatt for 1 hour, you will be charged for 1 "kilowatt-hour" of electricity. Suppose that the average consumption rate for a certain home is modeled by the function $$C(t) = 3.9 - 2.4sin(\frac{\pi*t}{12})$$ where C(t) is measured in kilowatts and t is the number of hours past midnight. Find the average daily consumption for this home, measured in kilowatt-hours.
Here's what I know:
The function is over the interval [0,24] and we need an integral. We also need the formula to find the average value of a function. Here's my equation:
$$\frac{1}{24}\int_{0}^{24}3.9 - 2.4sin(\frac{\pi*t}{12})dt$$
Upon solving the integral, I get:
$$\frac{1}{24}(3.9t + \frac{28.8}{\pi}cos(\frac{\pi*t}{12})) [0,24]$$
Finally solving gives me:
$$t = 3.9 kilowatt-hours$$
Does this look right to anyone? Or wrong?
