Ex 7.8, 21 Choose the correct answer ∫_1^(√3)▒𝑑𝑥/(1 + 𝑥^2 ) equals (A) 𝜋/3 (B) 2𝜋/3 (C) 𝜋/6 (D) 𝜋/12 Let F(𝑥)=∫1▒𝑑𝑥/(1 + 𝑥^2 ) =tan^(−1)⁡𝑥 Hence, F(𝑥)=𝑡𝑎𝑛^(−1) 𝑥 Now ∫_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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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.

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