The diagram shows the curve with equation y = 3 sin x − 3 sin 2x for 0 ≤ x ≤ π. The curve meets the x-axis at the origin and at the points with x-coordinates a and π.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [1] Attempt to find x-value from 3sinx-3sin 2x = 0 using identity for sin 2x
2. [1] Obtain at least cosx = ½
3. [1] Obtain ⅓π SC B3 can be spotted from sin x = sin 2x
4. [1] Integrate to obtain form k₁ cosx + k₂ cos 2x non-zero constants k₁, k₂ M0 for 3cosx+6cos 2x
5. [1] Obtain correct -3cosx + (3/2)cos2x
6. [1] Attempt value of integral using their lower limit (in radians) and π correctly DM1 Allow one sign error
7. [1] Obtain 27/4 OE