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令x=asint
则原式=∫(0→π/2)a^2sin^2(t)/(acost)*acostdt
=a^2∫(0→π/2)sin^2(t)dt
=a^2∫(0→π/2)(1-cos(2t))/2dt
=a^2/2∫(0→π/2)dt-a^2/2∫(0→π/2)cos(2t)dt
=a^2/2t|(0→π/2)-a^2/4sin(2t)|(0→π/2)
=a^2/4*π
则原式=∫(0→π/2)a^2sin^2(t)/(acost)*acostdt
=a^2∫(0→π/2)sin^2(t)dt
=a^2∫(0→π/2)(1-cos(2t))/2dt
=a^2/2∫(0→π/2)dt-a^2/2∫(0→π/2)cos(2t)dt
=a^2/2t|(0→π/2)-a^2/4sin(2t)|(0→π/2)
=a^2/4*π
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