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Section 3.2 – Calculating Areas; Riemann Sums

Section 3.2 – Calculating Areas; Riemann Sums. Pick up notes out of your folder. 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 (3.2) Right Hand Sum (3.2) Midpoint Sum (3.2, 7.6)

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Section 3.2 – Calculating Areas; Riemann Sums

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  1. Section 3.2 – Calculating Areas; Riemann Sums Pick up notes out of your folder

  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 (3.2) Right Hand Sum (3.2) Midpoint Sum (3.2, 7.6) Trapezoidal Rule (3.2, 7.6)

  4. CALCULATOR REQUIRED 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)

  5. CALCULATOR REQUIRED 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)

  6. 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)

  7. CALCULATOR REQUIRED Approximate using trapezoidal approximation with four equal subintervals

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

  9. The table below shows the velocity of a child sliding down a giant “Water Splash” a) Sketch a velocity-time graph by plotting and connecting the data points

  10. The table below shows the velocity of a child sliding down a giant “Water Splash” b) On the graph, show the lower and upper estimates and the difference between them. Give lower and upper estimates of the distance traveled in 10 seconds

  11. Consider the function f of which a partial table of values is shown. If f is continuous, use the Trapezoid rule with n = 4 to estimate the value of

  12. Calculator Required

  13. CALCULATOR REQUIRED

  14. Calculator Required 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

  15. The graph of a function f whose domain is the interval [-4, 4] is shown below. Which of the following statements is/are true? • I only • B. I and II only • C. II and III only • D. I and III only • E. I, II, III

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