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Question 20 - 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 20

Evaluate: Definite Integration -1 → 1  ∫ (x + |x| + 1) / (x 2  + 2|x| + 1)

Transcript

Question 20 Evaluate: ∫1_(−1)^1▒(𝑥+|𝑥|+1)/(𝑥^2+2|𝑥|+1) We know that |𝑥|={█(−&𝑥, 𝑥<0@&𝑥, 𝑥≥0)┤ So, for –1 to 0, |x| = –x and for 0 to 1 |x| = x So, our integral becomes ∫1_(−1)^1▒(𝑥+|𝑥|+1)/(𝑥^2+2|𝑥|+1) ∫1_(−1)^0▒(𝑥+|𝑥|+1)/(𝑥^2+2|𝑥|+1) ∫1_0^1▒(𝑥+|𝑥|+1)/(𝑥^2+2|𝑥|+1) ∫1_(−1)^0▒(𝑥−𝑥+1)/(𝑥^2−2𝑥+1) ∫1_0^1▒(𝑥+𝑥+1)/(𝑥^2+2𝑥+1) ∫1_(−1)^0▒1/(𝑥^2−2𝑥+1) ∫1_0^1▒(2𝑥+1)/(𝑥^2+2𝑥+1) ∫1_(−1)^0▒1/(𝑥−1)^2 ∫1_0^1▒(2𝑥+1)/(𝑥+1)^2 ∫1_(−1)^0▒1/(𝑥−1)^2 ∫1_0^1▒(2𝑥+1+1−1)/(𝑥+1)^2 ∫1_(−1)^0▒1/(𝑥−1)^2 ∫1_0^1▒(2𝑥+2−1)/(𝑥+1)^2 ∫1_(−1)^0▒1/(𝑥−1)^2 ∫1_0^1▒(2(𝑥+1)−1)/(𝑥+1)^2 ∫1_(−1)^0▒1/(𝑥−1)^2 ∫1_0^1▒(2(𝑥+1) )/(𝑥+1)^2 ∫1_0^1▒1/(𝑥+1)^2 ∫1_(−1)^0▒1/(𝑥−1)^2 ∫1_0^1▒(2 )/((𝑥+1) ) ∫1_0^1▒1/(𝑥+1)^2 ∫1_(−1)^0▒1/(𝑥−1)^2 2 ∫1_0^1▒"dx " /((𝑥+1) ) ∫1_0^1▒1/(𝑥+1)^2 [(𝑥−1)^(−1)/(−1)]_(−1)^0 2[ln⁡〖|𝑥+1|〗 ]_0^1 [(𝑥+1)^(−1)/(−1)]_0^1 [(−1)/((𝑥−1))]_(−1)^0 "2" [ln⁡〖|𝑥+1|〗 ]_0^1 [(−1)/((𝑥+1))]_0^1 [(−1)/((0−1))−(−1)/((−1−1))] 2[ln⁡〖|2|〗−log⁡〖|1|〗 ] [(−1)/((1+1))−(−1)/((0+1))] [1−1/2] 2[ln⁡〖|2|〗−0] [−1/2+1] 1/2+2 ln⁡2−1/2 2 ln⁡2
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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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