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

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

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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: nd Graph (Table)

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

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Approximate using trapezoidal rule with four equal subintervals 1.Enter equation into y1 2.2 nd Window (Tblset) 3.Tblstart: 4 4.Tbl: nd 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 A. 21 B. 22 C. 23 D. 24 E. 25 X X X X X

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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 x024 f(x)

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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 A. 20 B. 21 C. 22 D. 23 E. 24 X X X X

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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 X1234 f(x)

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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

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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

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