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4 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 2 · Question 5(c)(ii)

A diagram shows part of the curve y² = 4x. P is the point on the curve at which the line y = 2x cuts the curve. The shaded area is bounded by y²=4x, y=2x and the x-axis.

Find the volume of the solid generated by rotating the shaded area through 2π radians about the x-axis.

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Other parts of this question

  1. 5(a)(i)State the value of lim(u→0) (sin u)/u.[1 mark]
  2. 5(a)(ii)By means of the substitution u = 3x, show that lim(x→0) (sin 3x)/x = 3.[4 marks]
  3. 5(a)(iii)Hence, evaluate lim(x→0) (sin 3x)/(sin 5x).[4 marks]
  4. 5(b)If y = A/x + Bx, where A and B are constants, show that x(d²y/dx²) + x(dy/dx) = y.[4 marks]
  5. 5(c)(i)Find the coordinates of P.[3 marks]

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