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

Ex 7.9, 10 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.9, 10 ∫_0^1▒𝑑π‘₯/(1 + π‘₯2) Let F(π‘₯)=∫1▒𝑑π‘₯/(1 + π‘₯^2 ) =∫1β–’1/(1^2 + π‘₯^2 ) 𝑑π‘₯ =1/1 .tan^(βˆ’1)⁑(π‘₯/1) =tan^(βˆ’1) π‘₯ Hence F(π‘₯)=tan^(βˆ’1) π‘₯ (Using ∫1β–’1/(π‘₯^2 + π‘Ž^2 ) 𝑑π‘₯=1/π‘Ž tan^(βˆ’1)⁑π‘₯) Now, ∫_0^1▒〖𝑑π‘₯/(1 + π‘₯^2 )=𝐹(1)βˆ’πΉ(0) γ€— =tan^(βˆ’1)⁑〖(1)βˆ’tan^(βˆ’1)⁑(0) γ€— =πœ‹/4βˆ’0 =𝝅/πŸ’

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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.