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WMA12/01 Jan 2023, Question 1: The Trapezium Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Use the tabulated values of f(x) at x = −1, −0.5, 0, 0.5, 1 with the trapezium rule to estimate integrals involving f, giving answers as required.

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

Part (a) · 3 marks

Apply the trapezium rule with all five y-values to estimate the integral of f(x) from −1 to 1, to 2 decimal places.

  1. 1Strip width h = 0.5
  2. 2∫ ≈ ½ × 0.5 × {2.287 + 2.834 + 2(4.470 + 6.719 + 7.291)}
  3. 3= 0.25 × {5.121 + 36.96} = 0.25 × 42.081
  4. 4= 10.52 (2 d.p.)

Answer10.52

Part (bi) · 2 marks

Use the part (a) estimate to find the integral from −1 to 1 of f(x) − 2.

  1. 1∫₋₁¹ (f(x) − 2) dx = ∫₋₁¹ f(x) dx − ∫₋₁¹ 2 dx
  2. 2∫₋₁¹ 2 dx = 2 × 2 = 4
  3. 3≈ 10.52 − 4 = 6.52

Answer6.52

Part (bii) · 1 mark

Use the part (a) estimate to find the integral from 1 to 3 of f(x − 2).

  1. 1y = f(x − 2) is y = f(x) translated 2 units right, so x = 1 to 3 matches x = −1 to 1
  2. 2∫₁³ f(x − 2) dx = ∫₋₁¹ f(x) dx ≈ 10.52

Answer10.52

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Also searched as: WMA12 January 2023 · WMA12/01 · wma12 jan23 · IAS Maths Pure Mathematics 2 January 2023 · question 1.
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