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

Ex 7.9, 21 - Chapter 7 Class 12 Integrals - Part 2


Ex 7.9, 21 Choose the correct answer ∫_1^(√3)▒𝑑π‘₯/(1 + π‘₯^2 ) equals (A) πœ‹/3 (B) 2πœ‹/3 (C) πœ‹/6 (D) πœ‹/12 Let F(π‘₯)=∫1▒𝑑π‘₯/(1 + π‘₯^2 ) =tan^(βˆ’1)⁑π‘₯ Hence, F(π‘₯)=π‘‘π‘Žπ‘›^(βˆ’1) π‘₯ Now ∫_1^(√3)▒〖𝑑π‘₯/(1 + π‘₯^2 )=𝐹(√3)βˆ’πΉ(1) γ€— =tan^(βˆ’1)β‘γ€–βˆš3βˆ’tan^(βˆ’1)⁑(1) γ€— =πœ‹/3βˆ’πœ‹/4 =πœ‹/12 ∴ Option (D) is correct.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.