Check sibling questions

Ex 7.2, 21 - Integrate tan2 (2x - 3) - Class 12 CBSE - Ex 7.2

Ex 7.2, 21 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.2, 21 - Chapter 7 Class 12 Integrals - Part 3

Learn Intergation from Davneet Sir - Live lectures starting soon!


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

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.