Ex 7.9, 10 - Direct Integrate dx / root 1 + x2  from 0 to 1 - Ex 7.9

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.9, 10 0﷮1﷮ 𝑑𝑥﷮ ﷮1+𝑥2﷯﷯﷯ Step 1 :- Let F 𝑥﷯= ﷮﷮ 𝑑𝑥﷮1 + 𝑥﷮2﷯﷯﷯ = ﷮﷮ 1﷮ 1﷮2﷯ + 𝑥﷮2﷯﷯﷯ 𝑑𝑥 = 1﷮1﷯ . tan﷮−1﷯﷮ 𝑥﷮1﷯﷯﷯ = tan﷮−1﷯ 𝑥 Hence F 𝑥﷯= tan﷮−1﷯ 𝑥 Step 2 :- 0﷮1﷮ 𝑑𝑥﷮1 + 𝑥﷮2﷯﷯=𝐹 1﷯−𝐹 0﷯﷯ = tan﷮−1﷯﷮ 1﷯− tan﷮−1﷯﷮ 0﷯﷯﷯ = 𝜋﷮4﷯−0 = 𝝅﷮𝟒﷯

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