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Misc 36 - Prove that x17 cos4 x dx = 0 - Class 12 Intgeration - Definate Integration by properties - P7

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Misc 36 Prove that ﷐−1﷮1﷮﷐𝑥﷮17﷯﷯﷐﷐cos﷮4﷯﷮𝑥﷯ 𝑑𝑥=0 Let 𝑓﷐𝑥﷯=﷐−1﷮1﷮﷐𝑥﷮17﷯﷯﷐﷐cos﷮4﷯﷮𝑥﷯ 𝑑𝑥 ∴ 𝑓﷐−𝑥﷯=﷐−1﷮1﷮﷐﷐−𝑥﷯﷮17﷯﷯﷐﷐cos﷮4﷯﷮﷐−𝑥﷯﷯ 𝑑𝑥 =﷐−1﷮1﷮﷐﷐﷐−1﷯﷮17﷯﷐𝑥﷯﷮17﷯﷯﷐﷐﷐𝑐𝑜𝑠 ﷮﷐−𝑥﷯﷯﷯﷮4﷯ 𝑑𝑥 =﷐−1﷮1﷮﷐−﷐𝑥﷯﷮17﷯﷯﷐﷐﷐cos﷮𝑥﷯﷯﷮4﷯ 𝑑𝑥 =−﷐−1﷮1﷮﷐𝑥﷮17﷯﷯﷐﷐cos﷮4﷯﷮𝑥﷯ 𝑑𝑥 Since 𝒇﷐𝒙﷯=−𝒇﷐−𝒙﷯ ∴ I=﷐−1﷮1﷮﷐𝑥﷮17﷯﷯﷐﷐𝑐𝑜𝑠﷮4﷯﷮𝑥﷯ 𝑑𝑥 =𝟎

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