CBSE Class 12 Sample Paper for 2023 Boards

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Question 9 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 2, 2026 by Teachoo

The value of ∫ ² ₃ x/x ² +1 dx is

(a) log⁡4

(b) log⁡3/2

(c) 1/2 log⁡2

(d) log⁡9/4

This question is Similar to Ex - 7.10 -1

[MCQ - Sample Paper] The value of ∫ x / x^2 + 1 dx from 2 -> 3 is - CBSE Class 12 Sample Paper for 2023 Boards

part 2 - Question 9 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 9 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

Question 9 The value of "∫" _2^3 𝑥/(𝑥^2+1) 𝑑𝑥 is (a) log⁡4 (b) log⁡〖3/2〗 (c) 1/2 log⁡2 (d) log⁡〖9/4〗We need to find ∫_𝟐^𝟑▒〖𝒙/(𝒙^𝟐 + 𝟏) 𝒅𝒙〗 Let 𝒕=𝒙^𝟐+𝟏 Differentiating w.r.t. 𝑥 𝑑𝑡/𝑑𝑥=𝑑/𝑑𝑥 (𝑥^2+1) 𝑑𝑡/𝑑𝑥=2𝑥 𝒅𝒕/𝟐𝒙=𝒅𝒙 Now, when 𝒙 varies from 2 to 3 then 𝒕 varies from 5 to 10 Therefore ∫_𝟐^𝟑▒〖𝒙/(𝒙^𝟐+𝟏) 𝒅𝒙=∫_𝟓^𝟏𝟎▒〖𝒙/𝒕 𝒅𝒕/𝟐𝒙〗〗 =1/2 ∫_5^10▒𝑑𝑡/𝑡 =𝟏/𝟐 [𝒍𝒐𝒈|𝒕|]_𝟓^𝟏𝟎 =1/2 [𝑙𝑜𝑔|10|−𝑙𝑜𝑔|5|] =1/2 [𝑙𝑜𝑔|10/5|] =1/2 𝑙𝑜𝑔|2| =𝟏/𝟐 𝒍𝒐𝒈 𝟐So, the correct answer is (c)

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Question 9 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

The value of ∫ 2 3 x/x 2 +1 dx is

(a) log⁡4

(b) log⁡3/2

(c) 1/2 log⁡2

(d) log⁡9/4

Davneet Singh

The value of ∫ ² ₃ x/x ² +1 dx is