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Ex 7.10, 1 - Evaluate definite integral x / x2 + 1 dx - Definate Integration - By Substitution

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.10, 1 Evaluate the integrals using substitution 0﷮1﷮ 𝑥﷮ 𝑥﷮2﷯ + 1﷯𝑑𝑥﷯ ﷮﷮ 𝑥﷮ 𝑥﷮2﷯+1﷯ 𝑑𝑥﷯ Put 𝑡= 𝑥﷮2﷯+1 Differentiating w.r.t.𝑥 𝑑𝑡﷮𝑑𝑥﷯= 𝑑﷮𝑑𝑥﷯ 𝑥﷮2﷯+1﷯ 𝑑𝑡﷮𝑑𝑥﷯=2𝑥 𝑑𝑡﷮2𝑥﷯=𝑑𝑥 Hence when 𝑥 varies from 0 to 1 then 𝑡 varies from 1 to 2 Therefore 0﷮1﷮ 𝑥﷮ 𝑥﷮2﷯+1﷯𝑑𝑥= 1﷮2﷮ 𝑥﷮𝑡﷯ 𝑑𝑡﷮2𝑥﷯﷯﷯ = 1﷮2﷯ 1﷮2﷮ 𝑑𝑡﷮𝑡﷯﷯ = 1﷮2﷯ 𝑙𝑜𝑔 𝑡﷯﷯﷮1﷮2﷯ = 1﷮2﷯ 𝑙𝑜𝑔 2﷯−𝑙𝑜𝑔 1﷯﷯ = 1﷮2﷯ 𝑙𝑜𝑔 2﷯−0﷯ = 1﷮2﷯𝑙𝑜𝑔 2﷯ = 𝟏﷮𝟐﷯𝒍𝒐𝒈 𝟐

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