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Section 8.5 Riemann Sums and the Definite Integral.

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Presentation on theme: "Section 8.5 Riemann Sums and the Definite Integral."— Presentation transcript:

1 Section 8.5 Riemann Sums and the Definite Integral

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 2.2 nd Window (Tblset) 3.Tblstart: 4 4.Tbl: nd Graph (Table)

5 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)

6 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)

7 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)

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

9 Approximate using trapezoidal rule with n = 4

10 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

11 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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