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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 * (1/2)hrs =2.5 kilowatt-hours.

Suppose the power use of a customer over a 30-day period is given by the continuous

function P(t) 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 days.

B.

Derive an expression representing the total number of kilowatt-hours used by the

customer in the 30-day period. (This expression should not be an approximation.)

for A:

I did R=720 sigma t=0 to t=720 f(t)

for B: i just did T(t)= integral sign 0 to 720 f(t)dt

Could someone confirm my answers? Thanks in advance.