Ex 7.2, 10 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 7.2, 10 Integrate the function: 1𝑥 − 𝑥 Step 1: Simplify the given function 1𝑥 − 𝑥 = 1 𝑥 𝑥 − 1 Step 2: 𝑥 − 1=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 12 . 𝑥 12 − 1−0= 𝑑𝑡𝑑𝑥 12 . 𝑥− 12= 𝑑𝑡𝑑𝑥 𝑑𝑥= 2 𝑑𝑡 𝑥− 12 𝑑𝑥=2 𝑥 𝑑𝑡 Step 3: Integrating the function 1𝑥 − 𝑥 . 𝑑𝑥 = 1 𝑥 𝑥 − 1 . 𝑑𝑥 putting 𝑡= 𝑥 − 1 & 𝑑𝑥=2 𝑥 𝑑𝑡 = 1 𝑥 𝑡 . 2 𝑥 . 𝑑𝑥 = 2𝑡 . 𝑑𝑡 = 2 1𝑡 . 𝑑𝑡 = 2 log 𝑡+𝐶 = 𝟐 𝒍𝒐𝒈 𝒙 −𝟏+𝑪
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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