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 Ex 7.2, 26 - Integrate cos root(x) / root x - Integration by substitution - Trignometric - Normal

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  1. Class 12
  2. Important Question for exams Class 12
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Ex 7.2, 26 cos﷮ ﷮𝑥﷯﷯﷮ ﷮𝑥﷯﷯ Step 1: Let ﷮𝑥﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1﷮2﷯﷯ 𝑥﷮ 1﷮2﷯ − 1﷯= 𝑑𝑡﷮𝑑𝑥﷯ 1﷮2﷯. 𝑥﷮− 1﷮2﷯﷯= 𝑑𝑡﷮𝑑𝑥﷯ 1﷮2 ﷮𝑥﷯﷯ = 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥 =2 ﷮𝑥﷯ . 𝑑𝑡 𝑑𝑥 =2𝑡 . 𝑑𝑡 Step 2: Integrating the function ﷮﷮ cos﷮ ﷮𝑥﷯﷯﷮ ﷮𝑥﷯﷯ ﷯. 𝑑𝑥 putting ﷮𝑥﷯=𝑡 & 𝑑𝑥=2𝑡 . 𝑑𝑡 = ﷮﷮ cos﷮𝑡﷯﷮𝑡﷯﷯. 2𝑡 . 𝑑𝑡 = ﷮﷮ 2 cos﷮𝑡﷯﷯. 𝑑𝑡 = 2 ﷮﷮ cos﷮𝑡﷯﷯. 𝑑𝑡 = 2 sin﷮𝑡﷯+𝐶 = 𝟐 𝒔𝒊𝒏﷮ ﷮𝒙﷯﷯+𝑪

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