∫(π/2:0)соs²x/2dx горю сррочно

Question

∫(π/2:0)соs²x/2dx горю сррочно

Answer 1

∫сos^2(x/2)dx [0;п/2] = ∫(1+cosx)/2 * dx [0;п/2] = 1/2 (x+sinx) [0;п/2] = x/2 + sinx/2 [0;п/2] = F(п/2) - F(0) = п/4 + sin(п/2)/2 - 0+0 = п/4 + 1/2