证明: (Ⅰ)∫0π/2lnsinxdx=∫0π/2lncosxdx; (Ⅱ)∫0π/2lnsin2xdx=∫0π/2lnsinxdx; (Ⅲ)∫0π/2lnsinxdx=-ln2.

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问题 证明:
(Ⅰ)∫0π/2lnsinxdx=∫0π/2lncosxdx;
(Ⅱ)∫0π/2lnsin2xdx=∫0π/2lnsinxdx;
(Ⅲ)∫0π/2lnsinxdx=-ln2.

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答案[*] (Ⅲ)由题(Ⅱ)与题(Ⅰ)得 [*]

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