# Section 7.6 – Numerical Integration

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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.

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

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

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)

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)

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)

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

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

Approximate using trapezoidal rule with n = 4

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

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

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

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

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

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

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

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

Trapezoidal Rule: Midpoint Rule

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

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

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