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Section 8.5 Riemann Sums and the Definite Integral

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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: 1 5.2 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: 1 5.2 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: 4.5 4.Tbl: 1 5.2 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: 1 5.2 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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1 Example 2 Estimate by the six Rectangle Rules using the regular partition P of the interval [0, ] into 6 subintervals. Solution Observe that the function.

1 Example 2 Estimate by the six Rectangle Rules using the regular partition P of the interval [0, ] into 6 subintervals. Solution Observe that the function.

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