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Ex 7.8, 10 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2023 by

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 7.8, 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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