Quelpr
7 marksIntegration II

CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2 · Question 2(c)(i)

Let I_n = \int_0^{\frac{\pi}{4}} \tan^n x\,dx, n \ge 2.

By using the result in (a) above, show that I_n + I_{n-2} = \frac{1}{n-1}.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 2(a)Show that for n \ge 2, \tan^n x = \tan^{n-2} x \sec^2 x - \tan^{n-2} x.[3 marks]
  2. 2(b)Find \frac{dy}{dx} when y = \tan^n x.[3 marks]
  3. 2(c)(ii)Hence evaluate I_4.[7 marks]

More practice: the rest of this paper · more Integration II questions · all CAPE Pure Mathematics Unit 2 past papers