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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.

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Presentation on theme: "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."— Presentation transcript:

1 Area under curves Consider the curve y = f(x) for x  [a, b] The actual area under the curve is units 2 The approximate area is the sum of areas of trapezoidal strips. Number of strips: Approximate area: units 2 Number of strips: Approximate area: units units units units units units units units units units units units units units units units units units 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 units 2 The approximate area with 20 trapezoidal strips is 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


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