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WMA11/01 Jun 2019, Question 4: Integration: Undoing Differentiation

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks

The question, in short

Find the indefinite integral of (4x² + 1) divided by 2√x with respect to x, giving the answer in its simplest form.

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Solution · 5 marks

  1. 1(4x² + 1)/(2√x) = 4x²/(2x^(1/2)) + 1/(2x^(1/2))
  2. 2= 2x^(3/2) + ½x^(−1/2)
  3. 3∫ 2x^(3/2) dx = 2 × x^(5/2)/(5/2) = (4/5)x^(5/2)
  4. 4∫ ½x^(−1/2) dx = ½ × x^(1/2)/(1/2) = x^(1/2)
  5. 5Answer: (4/5)x^(5/2) + x^(1/2) + c

Answer(4/5)x^(5/2) + x^(1/2) + c

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