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Ex 7.3, 11 - Integrate cos4 2x - Chapter 7 CBSE NCERT - Integration using trigo identities - 2x formulae

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Transcript

Ex 7.3, 11 cos﷮4﷯﷮2𝑥﷯ ﷮﷮ cos﷮4﷯﷮2𝑥﷯﷯𝑑𝑥 = ﷮﷮ cos﷮2﷯﷮2𝑥﷯﷯﷮2﷯﷯𝑑𝑥 = ﷮﷮ 1 + cos﷮4𝑥﷯﷮2﷯﷯﷮2﷯﷯ = ﷮﷮ 1﷮4﷯ 1+ cos﷮4𝑥﷯﷯﷮2﷯﷯ = ﷮﷮ 1﷮4﷯ 1﷮2﷯+ cos﷮4𝑥﷯﷯﷮2﷯+2 cos﷮4𝑥﷯﷯ 1﷯﷯﷯﷯𝑑𝑥 = 1﷮4﷯ ﷮﷮ 1+ cos﷮2﷯﷮4𝑥﷯+2 cos﷮4𝑥﷯﷯﷯𝑑𝑥 = 1﷮4﷯ ﷮﷮ 1+ cos 8𝑥 + 1﷮2﷯+2 cos﷮4𝑥﷯﷯﷯𝑑𝑥 = 1﷮4﷯ ﷮﷮1﷯𝑑𝑥+ 1﷮2﷯ ﷮﷮ cos 8𝑥+1﷯﷯𝑑𝑥+2 ﷮﷮ cos﷮4𝑥﷯﷯𝑑𝑥﷯ = 1﷮4﷯ ﷮﷮1﷯𝑑𝑥+ 1﷮2﷯ ﷮﷮ cos﷮8𝑥﷯﷯𝑑𝑥+ 1﷮2﷯ ﷮﷮1﷯𝑑𝑥+2 ﷮﷮ cos﷮4𝑥﷯﷯𝑑𝑥﷯ = 1﷮4﷯ 𝑥+ 1﷮2﷯ sin﷮8𝑥﷯﷮8﷯+ 1﷮2﷯𝑥+2 sin﷮4𝑥﷯﷮4﷯﷯+𝐶 = 1﷮4﷯ 𝑥+ 1﷮2﷯ 𝑥+ 1﷮16﷯ sin﷮8𝑥﷯+ 1﷮2﷯ sin﷮4𝑥﷯﷯+𝐶 = 1﷮4﷯ 3𝑥﷮2﷯ + 1﷮16﷯ sin﷮8𝑥﷯+ 1﷮2﷯ sin﷮4𝑥﷯﷯+𝐶 = 𝟑𝒙﷮𝟖﷯ + 𝟏﷮𝟖﷯ 𝒔𝒊𝒏﷮𝟒𝒙﷯+ 𝟏﷮𝟔𝟒﷯ 𝒔𝒊𝒏﷮𝟖𝒙﷯+𝑪

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