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Ex 7.2, 27 - Integrate root(sin 2x) cos 2x - Class 12 - Ex 7.2

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 27 ﷮𝑠𝑖𝑛2𝑥﷯ cos⁡2𝑥 Step 1: Let sin﷮2𝑥﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 cos﷮2𝑥﷯. 𝑑 2𝑥﷯﷮𝑑𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ cos﷮2𝑥﷯. 2= 𝑑𝑡﷮𝑑𝑥﷯ 2 cos﷮2𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 2 cos﷮2𝑥﷯.𝑑𝑥=𝑑𝑡 𝑑𝑥= 𝑑𝑡﷮2 cos﷮2𝑥﷯﷯ Step 2: Integrating the function ﷮﷮ ﷮𝑠𝑖𝑛2𝑥﷯ cos⁡2𝑥﷯. 𝑑𝑥 putting 𝑠𝑖𝑛﷮2𝑥﷯=𝑡 & 𝑑𝑥= 𝑑𝑡﷮2 cos﷮2𝑥﷯﷯ = ﷮﷮ ﷮𝑡﷯ cos⁡2𝑥﷯. 𝑑𝑡﷮2 cos﷮2𝑥﷯﷯ = ﷮﷮ ﷮𝑡﷯﷮2﷯﷯. 𝑑𝑡 = 1﷮2﷯ ﷮﷮ ﷮𝑡﷯﷯. 𝑑𝑡 = 1﷮2﷯ ﷮﷮ 𝑡﷯﷮ 1﷮2﷯﷯﷯ 𝑑𝑡 = 1﷮2﷯. 𝑡﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯﷯ +𝐶 = 1﷮2﷯ 𝑡﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯ +𝐶 = 1﷮3﷯ 𝑡﷮ 3﷮2﷯﷯+𝐶 = 𝐬𝐢𝐧﷮𝟐𝒙﷯﷯﷮ 𝟑﷮𝟐﷯﷯﷮𝟑﷯ +𝑪

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