请问划线部分,最后的π⼀4是怎样算出来的

2025-04-30 21:54:01
推荐回答(1个)
回答1:

a^2/4∫(0,π/2)sin^2xdx
=a^2/4∫(0,π/2)1/2(1-cos2x)dx
=a^2/4*1/2x|(0,π/2)-a^2/4*1/4∫(0,π/2)cos2xd(2x)
=a^2/4*1/2(π/2-0)-a^2/4*1/4sin2x|(0,π/2)
=a^2/4*π/4-a^2/4*1/4[sin2(π/2)-sin2*0]
=a^2/4*π/4-a^2/4*1/4[0-0]
=a^2/4*π/4