Section 7.6

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. 2nd Window (Tblset)
3. Tblstart 4
4. Tbl 1
5. 2nd Graph (Table)

5
Approximate using right-hand sums of
four rectangles of equal width

1. Enter equation into y1
2. 2nd Window (Tblset)
3. Tblstart 5
4. Tbl 1
5. 2nd Graph (Table)

6
Approximate using midpoint sums of
four rectangles of equal width

1. Enter equation into y1
2. 2nd Window (Tblset)
3. Tblstart 4.5
4. Tbl 1
5. 2nd Graph (Table)

7
Approximate using trapezoidal rule
with four equal subintervals

1. Enter equation into y1
2. 2nd Window (Tblset)
3. Tblstart 4
4. Tbl 1
5. 2nd Graph (Table)

8
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
9
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
10
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. 21 B. 22 C. 23 D. 24 E. 25
11
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
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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
13
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. 20 B. 21 C. 22 D. 23 E. 24
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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
X 1 2 3 4
f(x) 0 0.693 1.099 1.386
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Trapezoidal Rule
Midpoint Rule
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CALCULATOR REQUIRED
Determine how many subdivisions are required with
the Midpoint Rule to approximate the integral
below with error less than 0.001
152
17
CALCULATOR REQUIRED
Determine how many subdivisions are required with
the Trapezoid Rule to approximate the integral
below with error less than 0.01
26