证明:∫0π/2sinnxcossinnxdx=2sin-n∫0π/2sinsinnxdx.

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问题 证明:∫0π/2sinnxcossinnxdx=2sin-n0π/2sinsinnxdx.

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答案0π/2sinncosnxdx=2-n-10π/2sinn2xd(2x)=2-n-10πsinnxdx=2-n0π/2sinnxdx.

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