r=a(1+sinθ) (a>0)的曲线长度,是（ - 知识问答

r=a(1+sinθ) (a>0)的曲线长度,是（8×2½）a么?

1个回答

=a+asinθ
r'=acosθ
S=2∫(-π/2到π/2)√(r^2+r'^2)dθ
=2∫(-π/2到π/2)√[2a^2(sinθ+1)]dθ
=2∫(-π/2到π/2)√[2a^2(sin(θ/2)+cos(θ/2))^2]dθ
=2∫(-π/2到π/2)√2*a[sin(θ/2)+cos(θ/2)]dθ
=4√2*a[sin(θ/2)-cos(θ/2)](上π/2下-π/2)
=8a

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