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Ex 7.2, 6 - Integrate root(ax + b) - Chapter 7 Class 12 - 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, 6 Integrate the function: ﷮𝑎𝑥+𝑏﷯ Step 1: Let 𝑎𝑥 + 𝑏 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑎.1+0 = 𝑑𝑡﷮𝑑𝑥﷯ 𝑎= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮𝑎﷯ Step 2: Integrating the function ﷮﷮ ﷮𝑎𝑥+𝑏﷯ ﷯ .𝑑𝑥 putting 𝑡=𝑎𝑥+𝑏 & 𝑑𝑥= 𝑑𝑡﷮𝑎﷯ = ﷮﷮ ﷮𝑡﷯ ﷯ . 𝑑𝑡﷮𝑎﷯ = 1﷮𝑎﷯ ﷮﷮ ﷮𝑡﷯ ﷯ .𝑑𝑡 = 1﷮𝑎﷯ ﷮﷮ ﷯ 𝑡﷮ 1﷮2﷯﷯ .𝑑𝑡 = 1﷮𝑎﷯ 𝑡﷮ 1﷮2﷯ +1﷯﷮ 1﷮2﷯ +1﷯+𝐶1﷯ = 1﷮𝑎﷯ 𝑡﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯+𝐶1﷯ = 1﷮𝑎﷯ 2﷮3﷯. 𝑡﷮ 3﷮2﷯﷯+𝐶1﷯ = 2﷮3𝑎﷯. 𝑡﷮ 3﷮2﷯﷯ + 𝐶1﷮𝑎﷯ = 2﷮3𝑎﷯. 𝑡﷮ 3﷮2﷯﷯ + 𝐶 = 𝟐﷮𝟑𝒂﷯. 𝒂𝒙+𝒃﷯﷮ 𝟑﷮𝟐﷯﷯ + 𝑪

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