1. Section 7.6 – Numerical Integration

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 1.Enter equation into y1 2.2 nd Window (Tblset) 3.Tblstart: 4 4.Tbl: 1 5.2 nd Graph (Table)

5. Approximate using right-hand sums of four rectangles of equal width 1.Enter equation into y1 2.2 nd Window (Tblset) 3.Tblstart: 5 4.Tbl: 1 5.2 nd Graph (Table)

6. Approximate using midpoint sums of four rectangles of equal width 1.Enter equation into y1 2.2 nd Window (Tblset) 3.Tblstart: 4.5 4.Tbl: 1 5.2 nd Graph (Table)

7. Approximate using trapezoidal rule with four equal subintervals 1.Enter equation into y1 2.2 nd Window (Tblset) 3.Tblstart: 4 4.Tbl: 1 5.2 nd 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. Consider the function f whose graph is shown below. Use the Trapezoid Rule with n = 4 to estimate the value of A. 21 B. 22 C. 23 D. 24 E. 25 X X X X X

13. 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

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. 22.6 B. 22.9 C. 23.2 D. 23.5 E. 23.8 x024 f(x)12.6467.810

16. The graph of f over the interval [1, 9] is shown in the figure. Find a midpoint approximation with four equal subdivisions for A. 20 B. 21 C. 22 D. 23 E. 24 X X X X

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. 1.242 B. 2.485 C. 4.970 D. 7.078 E. 14.156 X1234 f(x)00.6931.0991.386

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