Show that ∫[from ¼π to ½π] (4 cos² 2x + 1/cos² x) dx = ¾√3 + ⅙π - 1.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [M1] Express 4cos² 2x in the form k₁ cos4x + k₂ where k₁k₂ ≠ 0 .
2. [A1] Obtain correct 2cos4x + 2 Allow unsimplified.
3. [B1] State or imply 1/cos² x = sec² x Maybe implied by integration.
4. [M1*] Integrate to obtain k₃ sin 4x + k₄x + tan x where k₃k₄ ≠ 0.
5. [A1] Obtain correctly ½sin 4x + 2x + tan x
6. [DM1] Use limits correctly with correct values of sin and tan indicated
7. [A1] Confirm given result ¾√3 + ⅙π - 1 with sufficient detail AG