令x=1/2*acosθ+1/2*a
y=1/2*a*sinθ
代入积分中得原式=∫√（1/2*a^2*cosθ+1/2*a^2）*√(1/4*a^2sin^2θ+1/4*a^2*cos^2θ)dθ
=1/2*a*√（1/2*a^2*(1+cosθ)dθ
=∫1/2*a^2*cos(θ/2)dθ 积分限为[0,π/3]
计算得a^2/4
令x=1/2*acosθ+1/2*a
y=1/2*a*sinθ
代入积分中得原式=∫√（1/2*a^2*cosθ+1/2*a^2）*√(1/4*a^2sin^2θ+1/4*a^2*cos^2θ)dθ
=1/2*a*√（1/2*a^2*(1+cosθ)dθ
=∫1/2*a^2*cos(θ/2)dθ 积分限为[0,π/3]
计算得a^2/4