Ex 7.9, 21 - Direct Integrate dx / 1 + x2 from 1 to root3 - Ex 7.9

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.9, 21 Choose the correct answer 1﷮ ﷮3﷯﷮ 𝑑𝑥﷮1 + 𝑥﷮2﷯﷯﷯ equals (A) 𝜋﷮3﷯ (B) 2𝜋﷮3﷯ (C) 𝜋﷮6﷯ (D) 𝜋﷮12﷯ Step 1 :- Let F 𝑥﷯= ﷮﷮ 𝑑𝑥﷮1 + 𝑥﷮2﷯﷯﷯ = tan﷮−1﷯﷮𝑥﷯ Hence F 𝑥﷯=𝑡𝑎 𝑛﷮−1﷯𝑥 Step 2 :- 1﷮ ﷮3﷯﷮ 𝑑𝑥﷮1 + 𝑥﷮2﷯﷯=𝐹 ﷮3﷯﷯−𝐹 1﷯﷯ = tan﷮−1﷯﷮ ﷮3﷯− tan﷮−1﷯﷮ 1﷯﷯﷯ = 𝜋﷮3﷯− 𝜋﷮4﷯ = 𝜋﷮12﷯ ∴ Option (D) is correct.

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