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1.12 I: Numerical methods (A-level only)

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Question 75
a.

Use the trapezium rule with 3 strips to estimate the value of

∫0π2cos⁡(x2)dx\displaystyle \int_0^{\pi} 2\cos\left(\frac{x}{2}\right)dx∫0π​2cos(2x​)dx

Give your answer to four decimal places.

[4]
b.

Find the exact value of ∫0π2cos⁡(x2)dx\displaystyle\int_0^{\pi} 2\cos\left(\frac{x}{2}\right)dx∫0π​2cos(2x​)dx.

[2]
c.

Hence find the percentage error in the estimate found in part (a), giving your answer to three significant figures.

[1]
Markscheme

1.12 I: Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.12 I: Numerical methods (A-level only)

125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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