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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2 · Question 6(c)

Given that f is an even function, show that integral from -a to a of f(x) dx = 2 * integral from 0 to a of f(x) dx.

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Other parts of this question

  1. 6(a)Calculate the volume of the solid generated by revolving the region bounded by the graphs of x = sqrt(y) and y = 2x about the y-axis.[7 marks]
  2. 6(b)Calculate the area between the line and the curve.[7 marks]
  3. 6(d)Solve the differential equation x^3 y' = 2 - x^4, given that at x = 1, y = 2.[6 marks]

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