When using the trapezium rule to estimate the area under a curve that is concave (curves downward, like an arch shape), which statement correctly describes the result?

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Question

When using the trapezium rule to estimate the area under a curve that is concave (curves downward, like an arch shape), which statement correctly describes the result?

Accepted Answer

B: The trapezium rule gives an underestimate of the true area — For a concave (arch-shaped) curve, the top of each trapezium lies below the curve, so the trapezium rule underestimates the true area. For a convex curve (bowl-shaped), the top of each trapezium lies above the curve, giving an overestimate. The trapezium rule is never exact for curves (only for straight lines) and can be applied to any continuous curve.

Answer

A: The trapezium rule gives an exact value for the area

Answer

B: The trapezium rule gives an underestimate of the true area

Answer

D: The trapezium rule cannot be applied to concave curves

Answer

C: The trapezium rule gives an overestimate of the true area

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