Chapter 7 Class 12 Integrals
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Ex 7.9, 1 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

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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

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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