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Ex 7.2, 18 - Integrate e tan-1 x / 1 + x2 - NCERT - Integration by substitution - Trignometric - Inverse

Ex 7.2, 18 - Chapter 7 Class 12 Integrals - Part 2


Transcript

Ex 7.2, 18 𝑒﷮ tan﷮−1﷯ 𝑥﷯﷮1 + 𝑥2﷯ Step 1: Let tan﷮−1﷯ 𝑥 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1﷮1 + 𝑥2﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥 = 1 + 𝑥2﷯𝑑𝑡 Step 2: Integrating the function ﷮﷮ 𝑒﷮ tan﷮−1﷯ 𝑥﷯﷮1 + 𝑥2﷯ ﷯. 𝑑𝑥 putting 𝑡𝑎𝑛﷮−1﷯ 𝑥=𝑡 & 𝑑𝑥= 1 + 𝑥2﷯𝑑𝑡 = ﷮﷮ 𝑒﷮𝑡﷯﷮1 + 𝑥2﷯﷯ . 1 + 𝑥2﷯𝑑𝑡 = ﷮﷮ 𝑒﷮𝑡﷯﷯ . 𝑑𝑡 = 𝑒﷮𝑡﷯+𝐶 = 𝒆﷮ 𝒕𝒂𝒏﷮−𝟏﷯ 𝒙﷯+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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.