Ex 7.2, 8 - Integrate x root(1 + 2x2) - Chapter 7 NCERT - Integration by substitution - x^n

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 8 Integrate the function: 𝑥 ﷮1+2𝑥2﷯ Step 1: Let 1 + 2𝑥2 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0+2.2𝑥 = 𝑑𝑡﷮𝑑𝑥﷯ 4𝑥= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮4𝑥﷯ Step 2: Integrating the function ﷮﷮ 𝑥 ﷮1+2𝑥2﷯﷯ . 𝑑𝑥 Putting 𝑡=1+2𝑥2 & 𝑑𝑥= 𝑑𝑡﷮4𝑥﷯ = ﷮﷮ 𝑥 ﷮𝑡﷯﷯ . 𝑑𝑡﷮4𝑥﷯ = 1﷮4﷯ ﷮﷮ ﷮𝑡﷯﷯ . 𝑑𝑡 = 1﷮4﷯ ﷮﷮ 𝑡﷮ 1﷮2﷯﷯﷯ . 𝑑𝑡 = 1﷮4﷯ . 𝑡﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯ + 𝐶 = 1﷮4﷯ . 𝑡﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯+𝐶 = 1﷮2﷯ . 𝑡﷮ 3﷮2﷯﷯﷮3﷯+𝐶 = 1﷮6﷯ . 𝑡﷮ 3﷮2﷯﷯+ 𝐶 = 𝟏﷮𝟔﷯ . 𝟏+𝟐 𝒙﷮𝟐﷯﷯﷮ 𝟑﷮𝟐﷯﷯+ 𝑪

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