Ex 7.1, 21 - Anti derivative of root (x) + 1/root x equals - Ex 7.1

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.1, 21 The anti derivative of ﷮𝑥﷯+ 1﷮ ﷮𝑥﷯﷯﷯ equals (A) 1﷮3﷯ x﷮ 1﷮3﷯﷯ + 2x 1﷮2﷯ + C (B) 2﷮3﷯ x 2﷮3﷯ + 1﷮2﷯ x2 + C (c) 2﷮3﷯ x 3﷮2﷯ +2x 1﷮2﷯ + C (D) 2﷮3﷯ x 3﷮2﷯ + 1﷮2﷯ x 1﷮2﷯ + C ﷮﷮ ﷮𝑥﷯+ 1﷮ ﷮𝑥﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ 𝑥﷮ 1﷮2﷯﷯+ 1﷮ 𝑥﷮ 1﷮2﷯﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ 𝑥﷮ 1﷮2﷯﷯+ 𝑥﷮ −1﷮2﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ 𝑥﷮ 1﷮2﷯﷯﷯𝑑𝑥+ ﷮﷮ 𝑥﷮ −1﷮2﷯﷯﷯𝑑𝑥 = 𝑥﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯ + 𝑥﷮ −1﷮2﷯ + 1﷯﷮ −1﷮2﷯ + 1﷯ + 𝐶 = 𝑥﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯ + 𝑥﷮ 1﷮2﷯﷯﷮ 1﷮2﷯﷯ + 𝐶 = 2﷮3﷯ 𝑥﷮ 3﷮2﷯﷯ +2 𝑥﷮ 1﷮2﷯﷯+ 𝐶 ∴ Option (C) is correct .

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