- Identify the strip width h and the number of strips n
- List the x-values at each strip boundary: x₀, x₁, x₂, ..., xₙ
- Calculate (or read from the graph) the y-value at each x-value
- Identify: first y-value = y₀, last y-value = yₙ, middle values = y₁ to yₙ₋₁
- Apply the formula: Area ≈ h/2 × (y₀ + yₙ + 2(y₁ + y₂ + ... + yₙ₋₁))
- Include units in your answer (e.g. m, km, litres)
Alternative approach: calculate each individual trapezium using Area = ½(a + b)h, then add them all up. This gives the same answer.
This deep dive covers Step-by-Step Process 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 5 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.