A-level · Integration

Integrating with trigonometric identitiesExam-style questions

Integrating trig functions that have no table entry by rewriting them first. Why sin²x is not ⅓sin³x; the cos 2x identities for squares of sine and cosine; exact values over an interval; tan² and cot² through the Pythagorean identities; products of sine and cosine through sin 2x; and squares of a multiple angle or a bracket.

Start practising Read the lesson

17 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 5

1
(a) Using the double-angle formula for cosine, show that

$\cos^2 x \equiv \dfrac{1 + \cos 2x}{2}$ . (2 marks)

The curve $S$ has equation $y = 6\cos^2 x$ , $\ 0 \le x \le \dfrac{\pi}{3}$ .(b) Find the exact area of the region bounded by $S$ , the coordinate axes and the line $x = \dfrac{\pi}{3}$ . (4 marks)
(c) The horizontal line $y = 3$ cuts $S$ at a single point in this interval. Find the exact area of the region enclosed by $S$ , the $y$ -axis and the line $y = 3$ . (4 marks)
Level 5 · 10 marksTry it