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4 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2007 · Paper 2 · Question 6(b)(i)

Sketch the curve y = x^2 + 4.

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  1. 6(a)(i)Use the result ∫_0^a f(x)dx = ∫_0^a f(a-x)dx, a > 0, to show that if I = ∫_0^(π/2) sin^2 x dx, then I = ∫_0^(π/2) cos^2 x dx.[2 marks]
  2. 6(a)(ii)Hence, or otherwise, show that I = π/4.[6 marks]
  3. 6(b)(ii)Calculate the volume created by rotating the plane figure bounded by x = 0, y = 4, y = 5 and the curve y = x^2 + 4 through 360° about the y-axis.[8 marks]

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