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Ex 7.2, 10 - Integrate 1/(x - root(x)) - Chapter 7 CBSE - Ex 7.2

Ex 7.2, 10 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.2, 10 - Chapter 7 Class 12 Integrals - Part 3


Transcript

Ex 7.2, 10 Integrate the function: 1﷮𝑥 − ﷮𝑥﷯﷯ Step 1: Simplify the given function 1﷮𝑥 − ﷮𝑥﷯﷯ = 1﷮ ﷮𝑥﷯ ﷮𝑥﷯ − 1﷯﷯ Step 2: ﷮𝑥﷯ − 1=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1﷮2﷯ . 𝑥﷮ 1﷮2﷯ − 1﷯−0= 𝑑𝑡﷮𝑑𝑥﷯ 1﷮2﷯ . 𝑥﷮− 1﷮2﷯﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 2 𝑑𝑡﷮ 𝑥﷮− 1﷮2﷯﷯﷯ 𝑑𝑥=2 ﷮𝑥﷯ 𝑑𝑡 Step 3: Integrating the function ﷮﷮ 1﷮𝑥 − ﷮𝑥﷯﷯﷯ . 𝑑𝑥 = ﷮﷮ 1﷮ ﷮𝑥﷯ ﷮𝑥﷯ − 1﷯﷯﷯ . 𝑑𝑥 putting 𝑡= ﷮𝑥﷯ − 1 & 𝑑𝑥=2 ﷮𝑥 ﷯ 𝑑𝑡 = ﷮﷮ 1﷮ ﷮𝑥﷯ 𝑡﷯﷯﷯ . 2 ﷮𝑥﷯ . 𝑑𝑥 = ﷮﷮ 2﷮𝑡﷯﷯ . 𝑑𝑡 = 2 ﷮﷮ 1﷮𝑡﷯﷯ . 𝑑𝑡 = 2 log﷮ 𝑡﷯﷯+𝐶 = 𝟐 𝒍𝒐𝒈﷮ ﷮𝒙﷯ −𝟏﷯﷯+𝑪

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.