证明：∫π0sinnxdx＝2∫π/20sinnxdx

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问题证明：∫_π⁰sinⁿxdx＝2∫_π/2⁰sinⁿxdx

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答案∫₀^πsinⁿxdx＝∫₀^π/2sinⁿxdx＋∫_π/2^πsinⁿxdx，而∫_π/2^πsinⁿxdx[*]∫₀^π/2sinⁿ(π－t)(－dt)＝∫₀^π/2sinⁿtdt＝∫₀^π/2sinⁿxdx 所以∫₀^πsinⁿxdx＝∫₀^π/2sinⁿxdx．

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数学

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