Question

Помогите пожалуйста )))

Answer 1

1) (-1/3)*интеграл(cos(2π/3 - 3x)d(2π/3 - 3x) = (-1/3)*sin(2π/3 - 3x) =(-1/3)*sin(2π/3 - 3π) + (1/3)*sin(2π/3) = (1/3)*sin(π/3) + (1/3)*sin(π/3) = (2/3)*(√3/2) = √3/3
2) (sinx + cosx)^2 = sin^2(x) + cos^2(x) + 2sinx*cosx = 1 + sin(2x)
интеграл(1 + sin(2x))dx = интеграл(1)dx + 0.5*интеграл(sin(2x))d(2x) = x - 0.5*cos(2x) = (π/2 - 0.5*cos(π)) - (0 - 0.5) = π/2 + 0.5 + 0.5 = 1 + π/2
3) 2sin^2(x/2) = 1 - cosx
интеграл(1 - cosx)dx = интеграл(1)dx - интеграл(cosx)dx = x - sinx = π/2 - sin(π/2) - (0 - sin0) = π/2 - 1