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

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

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问题 证明：∫0π/2sinnxcossinnxdx=2sin-n∫0π/2sinsinnxdx．
选项
答案∫0π/2sinncosnxdx=2-n-1∫0π/2sinn2xd(2x)=2-n-1∫0πsinnxdx=2-n∫0π/2sinnxdx．
解析
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考研数学二

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