Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.