# Misc 3 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 3 Integrate the function 1𝑥 𝑎𝑥 + 𝑥2 1𝑥 𝑎𝑥 + 𝑥2 𝑑𝑥 = 1𝑥 𝑥2 𝑎𝑥 − 1 𝑑𝑥 = 1𝑥 . 𝑥 𝑎𝑥 − 1 𝑑𝑥 = 1 𝑥2 𝑎𝑥 − 1 𝑑𝑥 Let 𝑎𝑥 −1=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 − 𝑎 𝑥2 −0 = 𝑑𝑡𝑑𝑥 − 𝑎 𝑥2 = 𝑑𝑡𝑑𝑥 𝑑𝑥 = − 𝑥2𝑎 . 𝑑𝑡 Putting the values of ax−1 and dx, we get 1 𝑥2 𝑎𝑥 − 1 𝑑𝑥 = 1 𝑥2 𝑡 𝑑𝑥 = 1 𝑥2 𝑡 × − 𝑥2𝑎 . 𝑑𝑡 = −1𝑎 𝑑𝑡 𝑡 = −1𝑎 𝑡− 12 𝑑𝑡 = −1𝑎 𝑡− 12 + 1− 12 + 1+𝐶 = −1𝑎 𝑡 12 12 + 𝐶 = −2𝑎 𝑡 + 𝐶 Putting back t = 𝑎𝑥−1 = −2𝑎 𝑎𝑥 −1 + 𝐶 = −𝟐𝒂 𝒂 − 𝒙𝒙 + 𝑪

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Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

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Davneet Singh

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.