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 Dec. 13, 2024 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

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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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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