Area under a curve and the trapezium rule

Pick a curve and a method and increase the number of strips.

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Questions students ask

What is the trapezium rule?

Area ≈ ½h[y₀ + 2(y₁ + … + yₙ₋₁) + yₙ], where h is the strip width.

When does the trapezium rule over-estimate?

When the curve is concave up (bends upwards), the straight tops lie above it.

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