Chapter 7 Class 12 Integrals
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Misc 34 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

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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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo