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Ex 7.2, 13 - Integrate x2/(2 + 3x3)3 - Chapter 7 Class 12 - Integration by substitution - x^n

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Slide44.JPG

  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 13 Integrate the function: 𝑥2﷮ 2 + 3 𝑥﷮3﷯﷯﷮3﷯﷯ Step 1: Let 2+3𝑥3=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0+3.3 𝑥﷮3−1﷯= 𝑑𝑡﷮𝑑𝑥﷯ 9 𝑥﷮2﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥 = 𝑑𝑡﷮9 𝑥﷮2﷯﷯ Step 2: Integrating the function ﷮﷮ 𝑥2﷮ 2 + 3 𝑥﷮3﷯﷯﷮3﷯﷯﷯ . 𝑑𝑥 putting 2 + 3 𝑥﷮3﷯=𝑡 & 𝑑𝑥= 𝑑𝑡﷮9 𝑥﷮2﷯﷯ = ﷮﷮ 𝑥2﷮ 𝑡﷯﷮3﷯﷯﷯ . 𝑑𝑥 = ﷮﷮ 𝑥2﷮ 𝑡﷯﷮3﷯﷯﷯ . 𝑑𝑡﷮9 𝑥﷮2﷯﷯ = 1﷮9﷯ ﷮﷮ 𝑑𝑡﷮ 𝑡﷮3﷯﷯﷯ = 1﷮9﷯ ﷮﷮ 𝑡﷮−3﷯.𝑑𝑡﷯ = 1﷮9﷯ 𝑡﷮−3 + 1﷯﷮ −3 +1﷯﷯ + 𝐶 = 1﷮9﷯ 𝑡﷮−2﷯﷮ −2﷯﷯ + 𝐶 = − 1﷮18﷯ 𝑡﷮−2﷯ + 𝐶 = − 1﷮18 𝑡﷮2﷯﷯ + 𝐶 = − 𝟏﷮𝟏𝟖 𝟐 + 𝟑 𝒙﷮𝟑﷯﷯﷮𝟐﷯﷯ + 𝑪

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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