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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · 2022 · Paper 2 · Question 6(a)

Using the substitution u = x^2 + 1, determine \int 4x(x^2 + 1)^5\, dx.

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  1. 6(b)The diagram below shows two curves, y = x + x^2 and y = x(3 - x). Calculate the area of the shaded region.[6 marks]
  2. 6(c)Calculate the volume of the solid generated by revolving the region bounded by the line y = 6x and the parabola y = 6x^2 about the x-axis.[6 marks]
  3. 6(d)Solve the differential equation \frac{dy}{dx} = \frac{x + 4x^2}{y^2}, given that y = 6 when x = 0.[8 marks]

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