Check sibling questions


Transcript

Ex 7.2, 21 tan﷮2﷯ (2𝑥 – 3) Let I = ﷮﷮ tan﷮2﷯ (2𝑥 – 3)﷯ . 𝑑𝑥 = ﷮﷮ sec﷮2﷯ 2𝑥 – 3﷯−1﷯ ﷯𝑑𝑥 = ﷮﷮ sec﷮2﷯ 2𝑥 – 3﷯ ﷯𝑑𝑥− ﷮﷮ 1﷯.𝑑𝑥 = ﷮﷮ sec﷮2﷯ 2𝑥 – 3﷯ ﷯𝑑𝑥 − 𝑥+𝐶1 Solving 𝐈1 I1 = ﷮﷮ sec﷮2﷯ 2𝑥 – 3﷯ ﷯𝑑𝑥 Let 2𝑥 – 3=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 2−0 = 𝑑𝑡﷮𝑑𝑥﷯ 2= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥 = 𝑑𝑡﷮2﷯ Thus, our equation becomes ∴ ﷮﷮ sec﷮2﷯ 2𝑥 – 3﷯ ﷯𝑑𝑥 = ﷮﷮ sec﷮2 ﷯𝑡 ﷯. 𝑑𝑡﷮2﷯ = 1﷮2﷯ ﷮﷮ sec﷮2 ﷯𝑡 ﷯.𝑑𝑡 = 1﷮2﷯ tan﷮𝑡﷯+𝐶2 = 1﷮2﷯ tan﷮ 2𝑥−3﷯﷯+ 𝐶2 Now, I = ﷮﷮ sec﷮2﷯ 2𝑥 – 3﷯ ﷯𝑑𝑥−𝑥+𝐶1 = I1 − 𝑥+𝐶1 = 1﷮2﷯ tan﷮ 2𝑥−3﷯﷯+ 𝐶2 −𝑥+𝐶1 = 𝟏﷮𝟐﷯ 𝒕𝒂𝒏﷮ 𝟐𝒙−𝟑﷯﷯ −𝒙+𝑪

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

About the Author

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo