Section 8.5 Riemann Sums and the Definite Integral

Section 8.5 Riemann Sums and the Definite Integral

represents the area between the curve 3/x and the x-axis from x = 4 to x = 8

Four Ways to Approximate the Area Under a Curve With Riemann Sums Left Hand Sum Right Hand Sum Midpoint Sum Trapezoidal Rule

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)

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)

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)

Approximate using trapezoidal rule with four equal subintervals • Enter equation into y1 • 2nd Window (Tblset) • Tblstart: 4 • Tbl: 1 • 2nd Graph (Table)

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

Approximate using trapezoidal rule with n = 4

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

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

Section 8.5 Riemann Sums and the Definite Integral