V=π∫(0到1)(arccosy)²dy
设arccosy=t,那么y=cost
V=π∫(π/2到0)t²dcost
=π[t²cost|(π/2到0)-2∫(π/2到0)tcostdt]
=-2π∫(π/2到0)tcostdt
=-2π∫(π/2到0)tdsint
=-2π[tsint|(π/2到0)-∫(π/2到0)sintdt]
=π²+∫(π/2到0)sintdt
=π²-cost|(π/2到0)
=π²-1
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