Misc 34 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Miscellaneous
Misc 1
Important
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
Misc 34 Prove that ∫_(−1)^1▒𝑥^17 cos^4𝑥 𝑑𝑥=0 Let 𝑓(𝑥)=∫_(−1)^1▒𝑥^17 cos^4𝑥 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 [cos𝑥 ]^4 𝑑𝑥 =−∫_(−1)^1▒𝑥^17 cos^4𝑥 𝑑𝑥 Since 𝒇(𝒙)=−𝒇(−𝒙) ∴ I=∫_(−1)^1▒𝑥^17 〖𝑐𝑜𝑠〗^4𝑥 𝑑𝑥 =𝟎
