Integration Full Chapter Explained - https://you.tube/Integration-Class-12

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

Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13

Misc 14 Important

Misc 15

Misc 16

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21

Misc 22

Misc 23 You are here

Misc 24 Important

Misc 25 Important

Misc 26 Important

Misc 27 Important

Misc 28 Important

Misc 29

Misc 30 Important

Misc 31 Important

Misc 32 Important

Misc 33 Important

Misc 34

Misc 35

Misc 36

Misc 37

Misc 38 Important

Misc 39

Misc 40 Important

Misc 41 Important

Misc 42

Misc 43

Misc 44 Important

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 9 years. He provides courses for Maths and Science at Teachoo.