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Question Number 153112 by peter frank last updated on 04/Sep/21

∫_(−π) ^π (sin^(75) x+x^(125) )dx=0

$$\int_{−\pi} ^{\pi} \left(\mathrm{sin}\:^{\mathrm{75}} \mathrm{x}+\mathrm{x}^{\mathrm{125}} \right)\mathrm{dx}=\mathrm{0} \\ $$

Answered by puissant last updated on 04/Sep/21

∫_(−a) ^a f(x)dx=0 if f(−x)=−f(x).

$$\int_{−{a}} ^{{a}} {f}\left({x}\right){dx}=\mathrm{0}\:{if}\:{f}\left(−{x}\right)=−{f}\left({x}\right). \\ $$

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