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WMA12/01 Jun 2021, Question 5: The Trapezium Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 10 marks

The question, in short

Use the table and the given curve equation to estimate areas: apply the trapezium rule to C₁, integrate C₂, then combine results to estimate the shaded region R between x = 2.5 and x = 4.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 4 marks

Apply the trapezium rule with all tabulated y values to estimate the area under C₁ from x = 2.5 to x = 4, giving the answer to 2 decimal places.

  1. 1h = 0.25
  2. 2Area ≈ (0.25/2) × {5.453 + 5 + 2(7.764 + 9.375 + 9.964 + 9.367 + 7.626)}
  3. 3= 0.125 × {10.453 + 88.192} = 0.125 × 98.645
  4. 4= 12.33 (2 d.p.)

Answer12.33

Part (b) · 3 marks

Integrate x^(3/2) − 3x + 9 with respect to x.

  1. 1Raise each power by 1 and divide by the new power
  2. 2x^(3/2) → x^(5/2) ÷ (5/2) = (2/5)x^(5/2)
  3. 3−3x → −(3/2)x² and 9 → 9x
  4. 4Answer: (2/5)x^(5/2) − (3/2)x² + 9x + c

Answer(2/5)x^(5/2) − (3/2)x² + 9x + c

Part (c) · 3 marks

Combine the part (a) and part (b) results to estimate the area of region R, to one decimal place.

  1. 1Area under C₂ from 2.5 to 4: [(2/5)x^(5/2) − (3/2)x² + 9x] from 2.5 to 4
  2. 2= 24.8 − 17.077… = 7.722…
  3. 3Area R ≈ 12.33 − 7.722 = 4.608…
  4. 4Area R ≈ 4.6

Answer4.6

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