令x=2sint
则原式=∫[4-4(sint)^2]^(1/2) d2sint 在0到π/6上的积分
∫[4-4(sint)^2]^(1/2) d2sint 0到π/6
=4∫(cost)^2dt 0到π/6
=∫(cos2t+1)d2t 0到π/6
=sin2t+2t 0到π/6
=π/3+2分之根号3
令x=2sint
则原式=∫[4-4(sint)^2]^(1/2) d2sint 在0到π/6上的积分
∫[4-4(sint)^2]^(1/2) d2sint 0到π/6
=4∫(cost)^2dt 0到π/6
=∫(cos2t+1)d2t 0到π/6
=sin2t+2t 0到π/6
=π/3+2分之根号3