Ex 7.10, 13 By using the properties of definite integrals, evaluate the integrals : ∫_((− 𝜋)/2)^(𝜋/2)▒sin^7⁡𝑥 𝑑𝑥 This is of form ∫_(−𝑎)^𝑎▒𝑓(𝑥)𝑑𝑥 𝑓(𝑥)=sin^7⁡𝑥 𝑓(−𝑥)=sin^7⁡(−𝑥)=(−𝑠𝑖𝑛𝑥)^7=(−1)^7 (𝑠𝑖𝑛𝑥)^7=−sin^7⁡𝑥 Thus, 𝑓(−𝑥) =−𝑓⁡(𝑥) ∴ ∫_((−𝜋)/2)^(𝜋/2)▒sin^7⁡〖𝑥 𝑑𝑥=𝟎〗

Next: Example 31 → Ask a doubt

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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.

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