1. Area under curves Consider the curve y = f(x) for x  [a, b] The actual area under the curve is 83.60 units 2 The approximate area is the sum of areas of trapezoidal strips. Number of strips: Approximate area: 1 63.59 units 2 Number of strips: Approximate area: 2 77.79 units 2 3 80.85 units 2 4 82.00 units 2 5 82.55 units 2 6 82.86 units 2 83.05 units 2 7 83.18 units 2 8 83.26 units 2 9 83.33 units 2 10 83.37 units 2 11 83.41 units 2 12 83.43 units 2 13 83.46 units 2 14 83.47 units 2 15 83.49 units 2 16 83.50 units 2 17 83.51 units 2 18 83.52 units 2 19 83.53 units 2 20 y = f(x) ab x y 0

2. Area under curves As the number of strips n becomes large, the approximate area approaches the actual area under the curve. The actual area under the curve is 83.60 units 2 The approximate area with 20 trapezoidal strips is 83.53 units 2 y = f(x) ab x y 0

3. Area under curves Approximate area under a curve (Cabri) Approximate area under a curve (Geometer’s sketchpad) Approximate area under a curve (Excel) Resources