1. Section 7.6 – Numerical Integration
I can integrate definite integrals using Left Hand Sum, Right Hand Sum, Midpoint Sum, and Trapezoidal Rule.
Day 5:
Fill in the blank (try to do it using your memory): 1. 2. 3.

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
Right Hand Sum
Midpoint Sum
Trapezoidal Rule

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)

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)

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

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

9. Approximate using trapezoidal rule with n = 4

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

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

12. The graph of f is shown to the right. Which of the following
Statements are true?
A. I only B. II only C. I and II only D. II and III only E. I, II, III

13. Consider the function f whose graph is shown below. Use the
Trapezoid Rule with n = 4 to estimate the value of X X X X X
A B C D E. 25

14. A graph of the function f is shown to the right. Which of the
statements are true?
A. I only B. II only C. I and II only D. II and III only E. I, II, III

15. CALCULATOR REQUIRED
A B C D E x 2 4
f(x) 1
2.646
7.810

16. The graph of f over the interval [1, 9] is shown in the figure.
Find a midpoint approximation with four equal subdivisions for X X X X
A B C D E. 24

17. CALCULATOR REQUIRED
Let R be the region in the first quadrant enclosed by the x-axis
and the graph of y = ln x from x = 1 to x = 4. If the Trapezoid
rule with three subdivisions is used to approximate the area of
R, the approximation is
A B C D E X 1 2 3 4
f(x)
0.693
1.099
1.386

18. Trapezoidal Rule:
Midpoint Rule

19. CALCULATOR REQUIRED
Determine how many subdivisions are required with the Midpoint
Rule to approximate the integral below with error less than 0.001
152

20. CALCULATOR REQUIRED
Determine how many subdivisions are required with the Trapezoid
Rule to approximate the integral below with error less than 0.01 26