Use trig identity before indefinite integration

Requires using a trigonometric identity (e.g. cos²x = (1+cos2x)/2, tan²x = sec²x - 1) to rewrite the integrand, then find an indefinite integral.

3 questions · Moderate -0.5

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CAIE P2 2010 November Q4
6 marks Moderate -0.3
4
  1. Find \(\int \mathrm { e } ^ { 1 - 2 x } \mathrm {~d} x\).
  2. Express \(\sin ^ { 2 } 3 x\) in terms of \(\cos 6 x\) and hence find \(\int \sin ^ { 2 } 3 x \mathrm {~d} x\).
Edexcel P3 2023 January Q8
5 marks Moderate -0.8
  1. Find, in simplest form,
$$\int ( 2 \cos x - \sin x ) ^ { 2 } d x$$
SPS SPS SM 2021 November Q9
7 marks Moderate -0.3
    1. Show that \(\cos^2 x \equiv \frac{1}{2} + \frac{1}{2}\cos 2x\) [1]
    2. Hence find \(\int 2\cos^2 4x \, dx\) [3]
  2. Find \(\int \sin^3 x \, dx\) [3]