Check sibling questions

Ex 7.6, 11 - Integrate x cos-1 x / root 1 - x2 - Integration by parts

Ex 7.6, 11 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.6, 11 - Chapter 7 Class 12 Integrals - Part 3

Learn Intergation from Davneet Sir - Live lectures starting soon!


Transcript

Ex 7.6, 11 𝑥 cos﷮−1﷯﷮𝑥﷯﷮ ﷮1 − 𝑥﷮2﷯﷯﷯ Let cos﷮−1﷯﷮𝑥﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 −1﷮ ﷮1 − 𝑥﷮2﷯﷯﷯ = 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥=− ﷮1 − 𝑥﷮2﷯﷯ 𝑑𝑡 Putting the value of cos﷮−1﷯﷮x﷯ = t and dx = − ﷮1− x﷮2﷯﷯ dt , we get ﷮﷮ 𝑥 cos﷮−1﷯﷮𝑥﷯﷮ ﷮1 − 𝑥﷮2﷯﷯﷯﷯ .𝑑𝑥 = ﷮﷮ 𝑥 . 𝑡﷮ ﷮1 − 𝑥﷮2﷯﷯﷯﷯ .𝑑𝑥 = ﷮﷮ 𝑥 . 𝑡﷮ ﷮1 − 𝑥﷮2﷯﷯﷯﷯ . − ﷮1 − 𝑥﷮2﷯﷯﷯𝑑𝑡 = ﷮﷮−𝑥𝑡 . 𝑑𝑡﷯ = − ﷮﷮𝑥𝑡 . 𝑑𝑡﷯ = − ﷮﷮ cos﷮𝑡﷯﷯𝑡 . 𝑑𝑡﷯ = − ﷮﷮𝑡 cos﷮𝑡﷯. 𝑑𝑡﷯ =− 𝑡 ﷮﷮ cos﷮𝑡﷯. 𝑑𝑡﷯− ﷮﷮ 𝑑𝑡﷮𝑑𝑡﷯ ﷮﷮ cos﷮𝑡﷯. 𝑑𝑡﷯﷯𝑑𝑡﷯﷯ =− 𝑡 sin﷮𝑡﷯− ﷮﷮1 . sin﷮𝑡﷯𝑑𝑡﷯﷯ =− 𝑡 sin﷮𝑡﷯− − cos﷮𝑡﷯﷯﷯+𝐶 =− 𝑡 sin﷮𝑡﷯+ cos﷮𝑡﷯﷯+𝐶 =−𝑡 sin﷮𝑡﷯− cos﷮𝑡﷯+𝐶 =−𝑡 ﷮1− 𝑐𝑜𝑠﷮2﷯﷯𝑡 −𝑐𝑜𝑠𝑡+𝐶 = − cos﷮−1﷯﷮𝑥﷯ ﷮1− 𝑥﷮2﷯﷯−𝑥+𝐶 = − ﷮1− 𝑥﷮2 ﷯﷯ cos﷮−1﷯﷮𝑥﷯+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.