Quelpr
6 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 6(a)(iii)

A diagram, not drawn to scale, is a sketch of the section of the function f(x) = x(x² - 12) which passes through the origin O. A and B are stationary points on the curve.

Find the area between the curve and the positive x-axis.

This question uses a figure or table from the paper — you'll see it when you practise.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 6(a)(i)Find the coordinates of each of the stationary points A and B[8 marks]
  2. 6(a)(ii)Find the equation of the normal to the curve f(x) = x(x² - 12) at the origin, O[2 marks]
  3. 6(b)(i)Use the result ∫(from 0 to a) f(x) dx = ∫(from 0 to a) f(a-x) dx, where a > 0, to show that ∫(from 0 to π) x sin x dx = ∫(from 0 to π) (π - x) sin x dx.[2 marks]
  4. 6(b)(ii)a)Show that ∫(from 0 to π) x sin x dx = ∫(from 0 to π) sin x dx - ∫(from 0 to π) x sin x dx[2 marks]
  5. 6(b)(ii)b)Show that ∫(from 0 to π) x sin x dx = π.[5 marks]

More practice: the rest of this paper · more Integration I questions · all CAPE Pure Mathematics Unit 1 past papers