Ex 7.6, 3 - Integrate x2 ex - Chapter 7 CBSE NCERT - Ex 7.6

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Ex 7.6, 3 𝑥﷮2﷯ 𝑒𝑥 ﷮﷮ 𝑥﷮2﷯ 𝑒𝑥 ﷯ 𝑑𝑥 ﷮﷮ 𝑥﷮2﷯ 𝑒𝑥 ﷯ 𝑑𝑥 = 𝑥﷮2﷯ ﷮﷮𝑒𝑥﷯𝑑𝑥− ﷮﷮ 𝑑 𝑥﷮2﷯﷯﷮𝑑𝑥﷯ ﷮﷮𝑒𝑥 𝑑𝑥﷯﷯﷯𝑑𝑥 = 𝑥﷮2﷯. 𝑒𝑥 − ﷮﷮2𝑥 . 𝑒𝑥﷯𝑑𝑥 = 𝑥﷮2﷯. 𝑒𝑥 −2 ﷮﷮𝑥 . 𝑒𝑥﷯𝑑𝑥 Thus, our equation becomes ∴ ﷮﷮ 𝑥﷮2﷯ 𝑒𝑥 ﷯ 𝑑𝑥= 𝑥﷮2﷯. 𝑒𝑥 −2 ﷮﷮𝑥 . 𝑒𝑥﷯𝑑𝑥 = 𝑥﷮2﷯. 𝑒𝑥 −2 𝑥 ﷮﷮𝑒𝑥﷯𝑑𝑥− ﷮﷮ 𝑑𝑥﷮𝑑𝑥﷯ ﷮﷮ 𝑒﷮𝑥﷯﷯𝑑𝑥﷯﷯𝑑𝑥﷯ = 𝑥﷮2﷯. 𝑒𝑥 −2 𝑥 𝑒𝑥− ﷮﷮1. 𝑒﷮𝑥﷯﷯𝑑𝑥﷯ = 𝑥﷮2﷯. 𝑒𝑥 −2 𝑥 𝑒𝑥− 𝑒﷮𝑥﷯﷯+𝐶 = 𝑥﷮2﷯. 𝑒𝑥 −2𝑥 𝑒𝑥− 2𝑒﷮𝑥﷯+𝐶 =𝒆𝒙 𝒙﷮𝟐﷯−𝟐𝒙+𝟐﷯+𝑪

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.