Ex 7.11, 14 - Using properties, evaluate integral cos5 x dx - Ex 7.11

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  1. Chapter 7 Class 12 Integrals
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Ex 7.11, 14 By using the properties of definite integrals, evaluate the integrals : 0﷮2𝜋﷮ cos﷮5﷯﷮𝑥﷯﷯ 𝑑𝑥 0﷮2𝜋﷮ cos﷮5﷯﷮𝑥﷯﷯ 𝑑𝑥 = 0﷮𝜋﷮ cos﷮5﷯﷮𝑥﷯﷯ 𝑑𝑥+ 0﷮𝜋﷮(2π−𝑥)﷯ 𝑑𝑥 = 0﷮𝜋﷮ 𝑐𝑜𝑠﷮5﷯𝑥 𝑑𝑥+ 0﷮𝜋﷮ 𝑐𝑜𝑠﷮5﷯﷯﷯ 𝑥 = 2 0﷮𝜋﷮ 𝑐𝑜𝑠﷮5﷯𝑥 𝑑𝑥﷯ = 2 0﷮ 𝜋﷮2﷯﷮ 𝑐𝑜𝑠﷮5﷯𝑥 𝑑𝑥+ 0﷮ 𝜋﷮2﷯﷮ cos﷮ 𝜋−𝑥﷯﷯ ﷯﷯𝑑𝑥﷯ = 2 0﷮ 𝜋﷮2﷯﷮ 𝑐𝑜𝑠﷮5﷯𝑥 𝑑𝑥+ 0﷮ 𝜋﷮2﷯﷮ − cos𝑥﷯﷮5﷯﷮𝑑𝑥﷯ ﷯﷯﷯ = 2 0﷮ 𝜋﷮2﷯﷮ 𝑐𝑜𝑠﷮5﷯𝑥﷯𝑑𝑥−2 0﷮ 𝜋﷮2﷯﷮ 𝑐𝑜𝑠﷮5﷯﷯𝑥 = 0

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