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Riemann Sums and the Definite Integral. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8.

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Presentation on theme: "Riemann Sums and the Definite Integral. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8."— Presentation transcript:

1 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 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)

5 Approximate using trapezoidal rule with four trapezoids of equal width

6 Approximate using trapezoidal rule with n = 4

7 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

8 If the velocity of a car is estimated at estimate the total distance traveled by the car from t = 4 to t = 10 using five trapezoids of equal width


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