Chapter 7 Class 12 Integrals
Concept wise

Example 31 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

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Example 31 Evaluate ∫_(−1)^1▒〖sin^5⁡𝑥 cos^4⁡𝑥 〗 𝑑𝑥 This is of form ∫_(−𝑎)^𝑎▒〖𝑓(𝑥)𝑑𝑥 〗 where 𝑓(𝑥)=sin^5⁡〖𝑥 cos^4⁡𝑥 〗 Finding 𝑓(−𝑥) 𝑓(−𝑥)=sin^5⁡〖(−𝑥) .cos^4⁡(−𝑥) 〗 𝑓(−𝑥)=[−sin⁡𝑥 ]^5 .cos^4⁡〖 (𝑥)〗 𝑓(−𝑥)=(−1)^5 sin^5⁡〖𝑥 .cos^4⁡𝑥 〗 𝑓(−𝑥)=−sin^5⁡〖𝑥 .cos^4⁡𝑥 〗 ∴ 𝑓(𝑥)=−𝑓(−𝑥) ∴ ∫_(−𝟏)^𝟏▒〖𝐬𝐢𝐧〗^𝟓⁡〖𝒙 〖𝐜𝐨𝐬〗^𝟒⁡〖𝒙 𝒅𝒙=𝟎〗 〗

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