✔ 最佳答案
四尖點內擺線, 又稱星形線, 有如忍者十字鏢.本曲線對稱於兩軸, 所以只算第一象線即可.其參數方程式如下:x = cos 3θy = sin 3θ0≦θ≦2π在第一象限, 0≦θ≦π/2, x = 0, θ =π/2; x = 1, θ = 0dx = - 3cos2θ sinθ dθ所求面積 =4∫10 y dx= 4∫π/20 sin3θ( -3c os2θ sinθ) dθ= 3∫0π/2 (2sinθ cosθ) 2 sin2θ dθ= 3∫0π/2 (sin 2 2θ)(1 – cos2θ) / 2 dθ= 3/2∫0π/2 [ (1 – cos4θ) / 2] - (sin 2 2θ cos2θ) dθ= 3/4 [θ - sin4θ / 4 - sin 2 2θ / 3) |0π/2 = 3π/ 8