May/June 2026 Paper 21

2026 · 7 questions · 15 parts · 50 marks

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5(a)5(b)5(c)5(d)

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Context for question 7

the curve $y=3+\sin^{2}2x-\cos2x$ for $0\le x\le\pi$, with two maximum points at $x=\alpha$ and $x=\beta$ and a dip between them, the region between the curve, the $x$-axis and the lines $x=\alpha$ and $x=\beta$ shaded grey, with axes labelled $x$, $y$ and origin $O$

The diagram shows the curve with equation

y = 3 + sin^{2} 2 x - cos 2 x

for

0 \leq x \leq π

. The

x

-coordinates of the two maximum points on the curve are

α

and

β

. The shaded region is bounded by the curve, the

x

-axis and the lines

x = α

and

x = β

.

7Areas Volumes Arc LengthHard9 marks

Find the exact area of the shaded region.

Exact area