₀∫π/6sin(x + π)cos(x + π)dx
3 3
= 1 ₀∫π/6sin(2x + 2π) + sin 0° dx
2
= 1 – 1/2 cos(2x + 2π/3) + 0 ]π/6
2 0
= – 1 cos 2x cos 2π/3 – sin 2x sin 2π/3 ]π/6
4 0
= – 1/4 (cos 2π/3 cos 2π/3 – sin 2π/6 sin 2π/3) – cos 0 cos 2π/3 – sin 0 sin 2π/3)
= – 1/4 1/2(- 1/2) – 1/2√3(1/2√3) – 1(-1/2) + 0
= – 1/4 – 1/4 – 3/4 + 1/2
= – 1/4 – 1/4 – 3/4 + 1/2
= -1/4(- 1/2)
= 1/8