∫(上限1/2,下限-1/2) ((arcsinx)^2/√(1-x^2) )dx答案是π/324

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∫(上限1/2,下限-1/2) ((arcsinx)^2/√(1-x^2) )dx答案是π/324

∫(上限1/2,下限-1/2) ((arcsinx)^2/√(1-x^2) )dx答案是π/324
∫(上限1/2,下限-1/2) ((arcsinx)^2/√(1-x^2) )dx
答案是π/324

∫(上限1/2,下限-1/2) ((arcsinx)^2/√(1-x^2) )dx答案是π/324
因为函数偶函数,所以
原式=2∫(上限1/2,下限0) ((arcsinx)^2/√(1-x^2) )dx
=2∫(上限1/2,下限0) ((arcsinx)^2darcsinx
=2/3 (arcsinx)³|(上限1/2,下限0)
=2/3*(π/6)³
=π/324