Moderate -0.8 This is a straightforward definite integral requiring only standard integration formulas for cos(2x) and sin(x), followed by substitution of limits. The reverse chain rule for cos(2x) is routine, and evaluating at the given limits involves standard exact values (π/6). This is simpler than an average A-level question as it requires no problem-solving—just direct application of memorized integration rules.
Substitute limits correctly in an integral of the form \(a\sin 2x + b\cos x\)
M1
Use correct exact values, e.g. of \(\cos\left(\frac{\pi}{6}\right)\)
M1
Obtain answer \(1 - \frac{1}{4}\sqrt{3}\), or equivalent
A1
[5]
Obtain integral $\frac{1}{2}\sin 2x - \cos x$ | B1 + B1 |
Substitute limits correctly in an integral of the form $a\sin 2x + b\cos x$ | M1 |
Use correct exact values, e.g. of $\cos\left(\frac{\pi}{6}\right)$ | M1 |
Obtain answer $1 - \frac{1}{4}\sqrt{3}$, or equivalent | A1 |
| [5] |