r=a(1+sinθ) (a>0)的曲线长度,是（8×2½）a么?
问题描述：
r=a(1+sinθ) (a>0)的曲线长度,是（8×2½）a么?
答
r=a+asinθr'=acosθS=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...