1. Section 3.2 – Calculating Areas; Riemann Sums
Pick up notes out of your folder

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

3. Four Ways to Approximate the Area Under a Curve
With Riemann Sums
Left Hand Sum (3.2)
Right Hand Sum (3.2)
Midpoint Sum (3.2, 7.6)
Trapezoidal Rule (3.2, 7.6)

4. CALCULATOR REQUIRED
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)

5. CALCULATOR REQUIRED
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)

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)

7. CALCULATOR REQUIRED
Approximate using trapezoidal approximation with four
equal subintervals

8. CALCULATOR REQUIRED
Approximate using left-hand sums of four rectangles of
equal width

9. The table below shows the velocity of a child sliding down a giant “Water Splash”
a) Sketch a velocity-time graph by plotting and connecting the data points

10. The table below shows the velocity of a child sliding down a giant “Water Splash”
b) On the graph, show the lower and upper estimates and the difference between them. Give lower and upper estimates of the distance traveled in 10 seconds

13. Consider the function f of which a partial table of values is shown.
If f is continuous, use the Trapezoid rule with n = 4 to estimate
the value of x 1 2 3 4 5 6 7 8 9
f(x)

14. Calculator Required x
f(x) 1 2
2.646 4
7.810

15. CALCULATOR REQUIRED

16. Calculator Required
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

17. The graph of a function f whose domain is the interval [-4, 4] is shown below. Which of the following statements is/are true?
I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, III