1. Riemann Sums and the Definite Integral1

2. represents the area between the curve 3/x and the x-axis
from x = 4 to x = 8 2

3. Four Ways to Approximate the Area Under a Curve
With Riemann Sums
Left Hand Sum
Right Hand Sum
Midpoint Sum
Trapezoidal Rule 3

4. Approximate using left-hand sums of four rectangles of equal width
Enter equation into y1
2nd Window (Tblset)
Tblstart: 4
Tbl: 1
2nd Graph (Table) 4

5. Approximate using right-hand sums of four rectangles of equal width
Enter equation into y1
2nd Window (Tblset)
Tblstart: 5
Tbl: 1
2nd Graph (Table) 5

6. Approximate using midpoint sums of four rectangles of equal width
Enter equation into y1
2nd Window (Tblset)
Tblstart: 4.5
Tbl: 1
2nd Graph (Table) 6

7. Approximate using trapezoidal rule with four equal subintervals
Enter equation into y1
2nd Window (Tblset)
Tblstart: 4
Tbl: 1
2nd Graph (Table) 7

8. Approximate using left-hand sums of four rectangles of equal width8

9. Approximate using trapezoidal rule with n = 49

10. For the function g(x), g(0) = 3, g(1) = 4, g(2) = 1, g(3) = 8,
g(4) = 5, g(5) = 7, g(6) = 2, g(7) = 4. Use the trapezoidal rule
with n = 3 to estimate 10

11. If the velocity of a car is estimated at
estimate the total distance traveled by the car from t = 4 to t = 10
using the midpoint sum with four rectangles 11