Question

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.)
C. Consider the following data for the function.
t f(x)
0 2.3
1 2.5
2 2.1
3 3.9
4 3.6
5 5.5
6 4.5
7 5.6
8 1.2
9 1.0
10 1.8

Recall that f(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.

I am trying and don't think i am getting the right answer.

Answer 1

well, you could choose a left Riemann sum or a right Riemann sum or an in between Riemann sum. For simplicity I will take the left
each day is 24 hours * 30 days = 720 hours
so
area = kw hr = p(0) + p(1) + p(2) ...+ p(719) [ each times one hour ]

B)
KwHr = integral from t = 0 to t = 720 of f(t) dt

your table I assume should show f(t) not f(x)
area = 2.3*1 + 2.5* 1 + 2.1*1 etc to 1.0 *1
because I am using the left sum option, I am not using (10, 1.8)
so add the first ten numbers to get your answer
I get 31.7 kw hr
which is about an average power of 3.17 kw during the ten hours.
It would be more accurate to then do a right sum using 1 to 10 and not using (0,2.3) then use the average of the right method and left method.

Answer 2

By the way

POWER IS NOT ENERGY

look in physics book NEVER in math book ! (mathematics text writers do not get this stuff. They do not know the difference between bearing and heading in navigation either)

Energy = power * time

in this problem
Energy is in KW HR
and Power is in KW

This sentence should be:

A kilowatt is a measure of how much power (******* leave that energy word OUT ***** ) a customer is using ...........