CAIE A-Level Mathematics 2.5.3 Trapezium Rule

Practise applying the trapezium rule with the correct interval width and endpoint weighting and judging over- or under-estimation from the curve's position relative to chords.

Exam points

calculate each required y-value and identify h from the bounds and number of intervals
apply the full h/2[y₀ + yₙ + 2(y₁ + ⋯ + yₙ₋₁)] formula with endpoints counted once
state over- or under-estimate by comparing the trapezium tops with the curve

[Maximum number: 3]

Figure for Question 2.5.3—Trapezium rule question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve with equation $y=\frac{2 \ln x}{3 x+1}$ . The curve crosses the x-axis at the point A and has a maximum point B. The shaded region is bounded by the curve and the lines x=3 and y=0.

Use the trapezium rule with two intervals to find an approximation to the area of the shaded region. Give your answer correct to 2 decimal places.

Use y-values [0], $\frac{2}{7} \ln 2$ or 0.1980 and $\frac{2}{10} \ln 3$ or 0.2197

B1

Use correct formula, or equivalent, with h=1

M1

Obtain 0.31

A1

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2.5.3—Trapezium rule question 1