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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


Transcript

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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