# Misc 23 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 23 Integrate the function tan−1 1 − 𝑥1 + 𝑥 Let x = cos 2𝜃 𝑑𝑥𝑑𝜃=−2 sin2𝜃 dx = −2 sin 2𝜃 d𝜃 Substituting, tan−1 1 − 𝑥1 + 𝑥 𝑑𝑥 = 𝑡𝑎𝑛−1 1 − cos2𝜃1 + cos2𝜃×(−2 sin2 𝜃) 𝑑 𝜃 = −2 𝑡𝑎𝑛−1 1 − 1 − 2 𝑠𝑖𝑛2 𝜃1 + 2 𝑐𝑜𝑠2 𝜃 − 1× sin 2𝜃 d𝜃 = −2 𝑡𝑎𝑛−1 sin2𝜃 cos2𝜃× sin2𝜃 𝑑𝜃 = −2 𝑡𝑎𝑛−1 sin𝜃 cos𝜃× sin2𝜃 𝑑𝜃 = −2 𝑡𝑎𝑛−1 𝑡𝑎𝑛𝜃× sin2𝜃 𝑑𝜃 = − 2 𝜃 sin2𝜃 𝑑𝜃 =−2 𝜃 sin2𝜃 𝑑𝜃− 𝑑 𝜃𝑑𝜃 sin2𝜃 𝑑𝜃 𝑑𝜃 =−2 𝜃 − cos2𝜃2− 1 − cos2𝜃2𝑑𝜃 =−2 −𝜃 cos2𝜃2+ cos2𝜃2𝑑𝜃 =−2 − 𝜃 cos2𝜃2+ sin2𝜃4 Now, x = cos 2𝜃 Putting the values = −2 − 12 12 𝑐𝑜𝑠−1𝑥𝑥+ 1 − 𝑥24 = −2 1 − 𝑥24− 𝑥 𝑐𝑜𝑠−1𝑥4+ C = 𝟏𝟐 𝒙 𝒄𝒐𝒔−𝟏𝒙− 𝟏− 𝒙𝟐 + C

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Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.