∫(0→π/4) cos²x dx
= ∫(0→π/4) (1 + cos2x)/2 dx
= ∫(0→π/4) 1/2 dx + ∫(0→π/4) 1/2 · cos2x (1/2)d(2x)
= 1/2 · π/4 + 1/4 · sin[2(π/4)]
= π/8 + 1/4