∫[0,a] √a^2 -x^2dx
首先算不定积分
∫√(a^2 -x^2)dx
设x=asinu,dx=acosudu,√(a^2 -x^2)=acosu
∫√(a^2 -x^2)dx
=∫acosuacosudu
=∫a^2cos^2udu
=∫a^2(1+cos2u)/2du
=a^2/4∫(1+cos2u)d(2u)
=a^2/4[2u+sin2u]
∫[0,a] √a^2 -x^2dx
首先算不定积分
∫√(a^2 -x^2)dx
设x=asinu,dx=acosudu,√(a^2 -x^2)=acosu
∫√(a^2 -x^2)dx
=∫acosuacosudu
=∫a^2cos^2udu
=∫a^2(1+cos2u)/2du
=a^2/4∫(1+cos2u)d(2u)
=a^2/4[2u+sin2u]