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Ex 7.10, 7 - Evaluate definite integral dx / x2 + 2x + 5 - Definate Integration - By Substitution

Ex 7.10, 7 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.10, 7 - Chapter 7 Class 12 Integrals - Part 3

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Transcript

Ex7.10, 7 Evaluate the integrals using substitution −1﷮1 ﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ + 2𝑥 + 5﷯﷯ we can write −1﷮1﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ + 2𝑥 + 5﷯= −1﷮1﷮ 𝑑𝑥﷮ 𝑥 + 2𝑥 + 1﷯ + 4﷯﷯﷯ = −1﷮1﷮ 𝑑𝑥﷮ 𝑥 + 1﷯﷮2﷯ + 2﷮2﷯﷯﷯ Putting 𝑥+1=𝑡 Differentiating w.r.t.𝑥 𝑑﷮𝑑𝑥﷯ 𝑥+1﷯= 𝑑𝑡﷮𝑑𝑥﷯ 1= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥=𝑑𝑡 Hence when 𝑥 varies from – 1 to 1 then 𝑡 varies from 0 to 2 Therefore, −1﷮1﷮ 𝑑𝑥﷮ 𝑥+1﷯﷮2﷯ + 2﷮2﷯﷯= 0﷮2﷮ 𝑑𝑡﷮ 𝑡﷮2﷯ + 2﷮2﷯﷯﷯﷯ = 1﷮2﷯ tan﷮−1﷯﷮ 𝑡﷮2﷯﷯﷯﷮0﷮2﷯ = 1﷮2﷯ tan﷮−1﷯﷮ 2﷮2﷯− 1﷮2﷯ tan﷮−1﷯﷮ 0﷮2﷯﷯﷯ = 1﷮2﷯ tan﷮−1﷯﷮1− 1﷮2﷯ tan﷮−1﷯﷮0﷯﷯ = 1﷮2﷯ × 𝜋﷮4﷯−0 = 𝝅﷮𝟖﷯

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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.