Area under a curve: integration and the trapezium rule
Fill the area under a curve with strips and compare the estimate with the exact definite integral as the strips get thinner.
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Questions students ask
What is the trapezium rule?
Area ≈ h/2 [y₀ + 2(y₁ + … + yₙ₋₁) + yₙ], adding the areas of trapezia of width h.
What does a definite integral represent?
The area between the curve and the x-axis between the two limits (counted negative below the axis).
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