The diagram shows the curve with equation y = √(1 + 3cos²(x)) for 0 ≤ x ≤ π. The region R is bounded by the curve, the axes and the line x = π. [Figure 10.1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [B1] Use y values 2, √2.5, 1 or equivalents
2. [M1] Use correct formula, or equivalent, with h = ½π and three y values
3. [A1] Obtain ½ × ½π(2 + 2√2.5 + 1) or equivalent and hence 4.84
4. [B1] State or imply volume is π∫(1+3cos²(½x)) dx Allow if π appears later; condone omission of dx
5. [M1] Use appropriate identity to express integrand in form k₁ + k₂ cos x
6. [A1] Obtain ∫π(½ + ¾cos x) dx or ∫(½ + ¾cos x) dx Condone omission of dx
7. [A1] Integrate to obtain π(½x + ¾sin x) or ½x + ¾sin x
8. [A1] Obtain ½π² with no errors seen