你这是贝努力双纽线,极坐标方程是ρ²=a²sin2θ 求面积时求一个叶的乘以2就可以了.
面积=2∫[0,π/2](1/2)ρ²dθ
=∫[0,π/2]a²sin2θdθ
=a²∫[0,π/2]sin2θdθ
=a²[(-1/2)cos2θ] [0,π/2]
=(-a²/2)[cosπ-cos0]
=a² 你这是贝努力双纽线,极坐标方程是ρ²=a²sin2θ 求面积时求一个叶的乘以2就可以了.
面积=2∫[0,π/2](1/2)ρ²dθ
=∫[0,π/2]a²sin2θdθ
=a²∫[0,π/2]sin2θdθ
=a²[(-1/2)cos2θ] [0,π/2]
=(-a²/2)[cosπ-cos0]
=a²