# Homework Help: Integration - Riemann Sums

1. Nov 22, 2009

### Physics197

1. The problem statement, all variables and given/known data

The following table shows the power produced by a 600kW wind turbine at the given wind speed and the number of hours the wind blows at that speed.
a) Plot the power characteristic as a function of wind speed.
b) Plot the wind duration curve as a function of wind speed.
c) Use a Riemann sum to verify that all 8760 hours in a year are accounted for.
d) Use a Riemann sum to calculate the total yearly energy capture for this wind location (remember energy = power x time).
e) If the power curve is p(t) and the wind duration curve is w(t), write the energy as an integral.

Wind Speed Wind duration Turbine output
m/s hours/year kW
0 0 0
2.5 1880 0
5 2580 10
7.5 2000 80
10 1300 220
12.5 650 400
15 290 550
17.5 60 600

2. Relevant equations

3. The attempt at a solution

I have already graphed a&b, How would you use riemann sums to show that all the hours are accounted for? Wouldn't you just add up the number of hours?

d & e are going over my head, but they don't seem to be hard