The trapezium rule uses straight-line tops instead of the actual curve, so it gives an approximation, not the exact answer.
- Underestimate: when the curve is concave UPWARD (curves up, like a bowl) — the straight tops of the trapezoids lie BELOW the curve
- Overestimate: when the curve is concave DOWNWARD (curves down, like a hill) — the straight tops lie ABOVE the curve
- To improve accuracy: use more strips (narrower h). The estimate gets closer to the exact area as h → 0
Exam tip: If asked "why is this an underestimate?", say: "The curve is concave upward, so the straight-line tops of the trapeziums lie below the actual curve, missing some area."
This deep dive covers Overestimate or Underestimate? within Area Under Curves for GCSE Mathematics. Revise Area Under Curves in Graphs for GCSE Mathematics with 9 exam-style questions and 10 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Area Under Curves
On a velocity-time graph, what does the area under the curve represent?
Explain whether the trapezium rule gives an overestimate or underestimate for the area under the curve y = x² between x = 0 and x = 3. Justify your answer.