Example 33 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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.

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