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Ex 7.2, 28 - Integrate cos x / root (1 + sin x) - Ex 7.2

Ex 7.2, 28 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.2, 28 - Chapter 7 Class 12 Integrals - Part 3

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Transcript

Ex 7.2, 28 cos﷮𝑥﷯﷮ ﷮1+ sin﷮𝑥﷯﷯﷯ Step 1: Let 1+ sin﷮𝑥﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0+cos 𝑥= 𝑑𝑡﷮𝑑𝑥﷯ cos﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮ cos﷮𝑥﷯﷯ Step 2: Integrating the function ﷮﷮ cos﷮𝑥﷯﷮ ﷮1 + sin﷮𝑥﷯﷯﷯ ﷯. 𝑑𝑥 putting 1+ 𝑠𝑖𝑛﷮𝑥﷯=𝑡 & 𝑑𝑥= 𝑑𝑡﷮ cos﷮𝑥﷯﷯ = ﷮﷮ cos﷮𝑥﷯﷮ ﷮𝑡﷯﷯﷯. 𝑑𝑡﷮ cos﷮𝑥﷯﷯ = ﷮﷮ 𝑑𝑡﷮ ﷮𝑡﷯﷯﷯ = ﷮﷮ 1﷮ 𝑡﷮ 1﷮2﷯﷯﷯ . 𝑑𝑡﷯ = ﷮﷮ 𝑡﷮− 1﷮2﷯ ﷯ . 𝑑𝑡﷯ = 𝑡﷮− 1﷮2﷯ + 1﷯﷮− 1﷮2﷯ + 1﷯ +𝐶 = 2. 𝑡﷮ 1﷮2﷯﷯ +𝐶 = 2 ﷮𝑡﷯ +𝐶 = 𝟐 ﷮𝟏+ 𝐬𝐢𝐧﷮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.