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Ex 7.2, 31 - Integrate sin x / (1 + cos x)2 - Ex 7.2

Ex 7.2, 31 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.2, 31 - Chapter 7 Class 12 Integrals - Part 3

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Transcript

Ex7.2, 31 sin﷮𝑥﷯﷮ 1+ cos﷮𝑥﷯﷯2﷯ Step 1: Let 1+ cos﷮𝑥﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0−sin 𝑥= 𝑑𝑡﷮𝑑𝑥﷯ − sin 𝑥= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥 = 𝑑𝑡﷮− sin 𝑥﷯ Step 2: Integrating the function ﷮﷮ sin﷮𝑥﷯﷮ 1+ cos﷮𝑥﷯﷯2﷯ ﷯. 𝑑𝑥 putting 1+ 𝑐𝑜𝑠﷮𝑥﷯=𝑡 & 𝑑𝑥= 𝑑𝑡﷮− sin 𝑥﷯ = ﷮﷮ sin﷮𝑥﷯﷮ 𝑡﷮2﷯﷯﷯ . 𝑑𝑡﷮− sin 𝑥﷯ = ﷮﷮ 1﷮− 𝑡﷮2﷯﷯﷯ = −1 ﷮﷮ 1﷮ 𝑡﷮2﷯﷯﷯ . 𝑑𝑡 = −1 𝑡﷮−2 +1﷯﷮−2 +1﷯ +𝐶 = −1 𝑡﷮−1﷯﷮−1﷯ +𝐶 = 𝑡﷮−1﷯ +𝐶 = 1﷮𝑡﷯ +𝐶 = 𝟏﷮𝟏+ 𝒄𝒐𝒔﷮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.