Misc 34 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

Misc 34 - Prove that x17 cos4 x dx = 0 - Class 12 Intgeration - Miscellaneous

part 2 - Misc 34 - Miscellaneous - Serial order wise - Chapter 7 Class 12 Integrals

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Misc 34 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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