Chapter 7 Class 12 Integrals
Concept wise

Ex 7.9, 1 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

Ex 7.9, 1 - Evaluate definite integral x / x2 + 1 dx - Ex 7.9 - Ex 7.9

part 2 - Ex 7.9, 1 - Ex 7.9 - Serial order wise - Chapter 7 Class 12 Integrals

Share on WhatsApp

Transcript

Ex 7.9, 1 Evaluate the integrals using substitution ∫_0^1▒〖𝑥/(𝑥^2 + 1) 𝑑𝑥〗 We need to find ∫_𝟎^𝟏▒〖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 0 to 1 then 𝒕 varies from 1 to 2 Therefore ∫_𝟎^𝟏▒〖𝒙/(𝒙^𝟐+𝟏) 𝒅𝒙=∫_𝟏^𝟐▒〖𝒙/𝒕 𝒅𝒕/𝟐𝒙〗〗 =1/2 ∫_1^2▒𝑑𝑡/𝑡 =𝟏/𝟐 [𝒍𝒐𝒈|𝒕|]_𝟏^𝟐 =1/2 [𝑙𝑜𝑔|2|−𝑙𝑜𝑔|1|] =1/2 [𝑙𝑜𝑔|2|−0] =1/2 𝑙𝑜𝑔|2| =𝟏/𝟐 𝒍𝒐𝒈 𝟐

Davneet Singh's photo - Co-founder, Teachoo

Made by

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