Misc 12 - Integrate x3 / root 1 - x8 - Chapter 7 NCERT - Miscellaneous

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Misc 12 Integrate the function 𝑥﷮3﷯﷮ ﷮1 − 𝑥﷮8﷯﷯﷯ ﷮﷮ 𝑥﷮3﷯﷮ ﷮1− 𝑥﷮8﷯﷯﷯𝑑𝑥=﷯ ﷮﷮ 𝑥﷮3﷯﷮ ﷮1 − 𝑥﷮4﷯﷯﷮2﷯﷯﷯𝑑𝑥﷯ Put 𝑥﷮4﷯=𝑡 Differentiating w.r.t.𝑥 4 𝑥﷮3﷯= 𝑑𝑡﷮𝑑𝑥﷯ d𝑥= 𝑑𝑡﷮4 𝑥﷮3﷯﷯ Therefore, ﷮﷮ 𝑥﷮3﷯﷮ ﷮1 − 𝑥﷮4﷯﷯﷮2﷯﷯﷯𝑑𝑥=﷯ ﷮﷮ 𝑥﷮3﷯﷮ ﷮1 − 𝑡﷮2﷯﷯﷯ 𝑑𝑡﷮4 𝑥﷮3﷯﷯﷯ = 1﷮4﷯ ﷮﷮ 𝑑𝑡﷮ ﷮1 − 𝑡﷮2﷯﷯﷯﷯ = 1﷮4﷯ sin﷮−1﷯﷮𝑡+𝑐﷯ Putting 𝑡= 𝑥﷮4﷯ = 𝟏﷮𝟒﷯ 𝒔𝒊𝒏﷮−𝟏﷯ 𝒙﷮𝟒﷯﷮+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.