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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 2 · Question 6(d)

Given that sin 2θ = 2 sin θ cos θ and cos 2θ = 1 - 2 sin² θ,

find ∫sin²x cos²x dx.

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Other parts of this question

  1. 6(a)(i)Determine the area of the region, A.[3 marks]
  2. 6(a)(ii)Calculate the volume of the solid that results from revolving the region, A, about the x-axis.[5 marks]
  3. 6(b)Given that the curve passes through the point (1,1), determine an expression for f(x).[7 marks]
  4. 6(c)By using the substitution, y = x², show that ∫ 1/(√y + √y³) dy = ∫ 2/(1 + x²) dx.[5 marks]

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