Question 7 - CBSE Class 12 Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

Question 7

Find: ∫ (x ² + sin ² ⁡x) sec ² ⁡x / (1 + x ² ) dx

Find integral (x^2 + sin^2 x) sec^2 x / (1 + x^2) - Teachoo

Question 7 - CBSE Class 12 Sample Paper for 2019 Boards - Part 2

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Transcript

Question 7 Find: ∫1▒((𝑥^2 + sin^2⁡𝑥 ) sec^2⁡𝑥)/(1 + 𝑥^2 ) dx ∫1▒((𝑥^2 + sin^2⁡𝑥 ) sec^2⁡𝑥)/(1 + 𝑥^2 ) dx = ∫1▒((𝑥^2 + sin^2⁡𝑥 )(1/cos^2⁡𝑥 ) )/(1 + 𝑥^2 ) dx = ∫1▒((𝑥^2 + sin^2⁡𝑥 ) )/((1 + 𝑥^2 ) cos^2⁡𝑥 ) dx Writing sin2 x = 1 – cos2 x = ∫1▒((𝑥^2 + 1 − cos^2⁡𝑥 ) )/((1 + 𝑥^2 ) cos^2⁡𝑥 ) dx = ∫1▒((1 + 𝑥^2 ) − cos^2⁡𝑥 )/((1 + 𝑥^2 ) cos^2⁡𝑥 ) dx = ∫1▒((1 + 𝑥^2 ) )/((1 + 𝑥^2 ) cos^2⁡𝑥 ) dx – ∫1▒(cos^2⁡𝑥 )/((1 + 𝑥^2 ) cos^2⁡𝑥 ) dx = ∫1▒1/cos^2⁡𝑥 dx – ∫1▒(1 )/((1 + 𝑥^2 ) ) dx = ∫1▒〖𝑠𝑒𝑐〗^2⁡𝑥 dx – ∫1▒(1 )/((1 + 𝑥^2 ) ) dx = 𝒕𝒂𝒏 𝒙−〖𝒕𝒂𝒏〗^(−𝟏) 𝒙 + C

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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