关于广义积分,1/(1-x^2)^1/2的广义积分,上限为1下限为0,是发散还是收敛?怎么算?

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关于广义积分,1/(1-x^2)^1/2的广义积分,上限为1下限为0,是发散还是收敛?怎么算?
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关于广义积分,1/(1-x^2)^1/2的广义积分,上限为1下限为0,是发散还是收敛?怎么算?
关于广义积分,
1/(1-x^2)^1/2的广义积分,上限为1下限为0,是发散还是收敛?怎么算?

关于广义积分,1/(1-x^2)^1/2的广义积分,上限为1下限为0,是发散还是收敛?怎么算?
∫1/(1-x^2)^1/2dx 令x=sint
dx=costdt
(1-x^2)^1/2=(1-(sint)^2)^1/2=((cost)^2)^1/2=cost
原式=∫dt (t从0到PI/2)
=PI/2

∫(0->1)1/(1-x^2)^1/2*dx=arcsin(x)(0->1)=π/2