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CBSE Class 12 Sample Paper for 2019 Boards

CBSE Class 12 Sample Paper for 2018 Boards →
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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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 May 29, 2023 by

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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