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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.

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**represents the area between the curve 3/x and the x-axis**

from x = 4 to x = 8

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**Four Ways to Approximate the Area Under a Curve**

With Riemann Sums Left Hand Sum Right Hand Sum Midpoint Sum Trapezoidal Rule

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**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)

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**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)

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**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)

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**Approximate using trapezoidal rule with four equal**

subintervals Enter equation into y1 2nd Window (Tblset) Tblstart: 4 Tbl: 1 2nd Graph (Table)

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**Approximate using left-hand sums of four rectangles of**

equal width

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**Approximate using trapezoidal rule with n = 4**

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**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

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**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

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**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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**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

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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

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

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**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

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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 B C D E X 1 2 3 4 f(x) 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

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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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Section 4.2 The Definite Integral. If f is a continuous function defined for a ≤ x ≤ b, we divide the interval [a, b] into n subintervals of equal width.

Section 4.2 The Definite Integral. If f is a continuous function defined for a ≤ x ≤ b, we divide the interval [a, b] into n subintervals of equal width.

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