这里的θ为x哦
{ r = 3cosθ
{ r = 1 + cosθ
3cosθ = 1 + cosθ
cosθ = 1/2
θ = π/3 或 2π - π/3 = 5π/3
交点为(3/2,π/3)和(3/2,5π/3)
∴阴影面积
= 2[∫(0→π/3) (1/2)(3cosθ)² dθ + ∫(π/3→π/2) (1/2)(1 + cosθ)² dθ]
= (9/2)∫(0→π/3) (1 + cos2θ) dθ + ∫(π/3→π/2) (1 + 2cosθ + cos²θ) dθ
= (9/2)[θ + sinθcosθ] |(0→π/3) + [θ + 2sinθ + (1/2)(θ + sinθcosθ)] |(π/3→π/2)
= (9/2)[π/3 + (√3/2)(1/2)] + [π/2 + 2 + (1/2)(π/2)] - [π/3 + √3 + (1/2)(π/3 + (√3/2)(1/2))]
= 2 + 7π/4
希望对你有所帮助