1. Power companies typically bill customers based on the number of kilowatt-hours used during a single billing period. A kilowatt is a measure of how much power (energy) a customer is using, while a kilowatt-hour is one kilowatt of power being used for one hour. For constant power use, the number of kilowatt-hours used is calculated by kilowatt-hours = kilowatts time (in hours). Thus, if customers use 5 kilowatts for 30 minutes, they'll have used 5 kilowatts hours = 2.5 kilowatt-hours. Suppose the power use of a customer over a 30-day period is given by the continuous function P = At), where P is kilowatts, t is time in hours, and t = 0 corresponds to the beginning of the 30 day period. A. Approximate, with a Riemann sum, the total number of kilowatt-hours used by the customer in the 30-day period, and explain why your Riemann sum is an approximation of the desired property. B. Derive an expression representing the total number of kilowatt-hours used by the customer in the 30-day period, and explain your reasoning. (This expression should not be an approximation.) C. Consider the following table of data for the functionflt). o 1 2 3 4 5 6 7 8 9 10 2.3 2.5 2.1 3.9 3.6 5.5 4.5 5.6 1.2 1.0 1.8 Recall thatJ(t) represents the number of kilowatts being used by a customer at time t hours from the beginning of the billing period. Estimate the number of kilowatt-hours the customer uses in this 10-hour period, and explain your method.